diff --git a/flang/lib/Semantics/resolve-names.cpp b/flang/lib/Semantics/resolve-names.cpp
--- a/flang/lib/Semantics/resolve-names.cpp
+++ b/flang/lib/Semantics/resolve-names.cpp
@@ -584,6 +584,7 @@
 protected:
   // Apply the implicit type rules to this symbol.
   void ApplyImplicitRules(Symbol &);
+  void AcquireIntrinsicProcedureFlags(Symbol &);
   const DeclTypeSpec *GetImplicitType(Symbol &, const Scope &);
   bool ConvertToObjectEntity(Symbol &);
   bool ConvertToProcEntity(Symbol &);
@@ -2146,7 +2147,7 @@
       }
       if (IsIntrinsic(symbol.name(), functionOrSubroutineFlag)) {
         // type will be determined in expression semantics
-        symbol.attrs().set(Attr::INTRINSIC);
+        AcquireIntrinsicProcedureFlags(symbol);
         return;
       }
     }
@@ -2157,6 +2158,24 @@
   }
 }
 
+// Ensure that the symbol for an intrinsic procedure is marked with
+// the INTRINSIC attribute.  Also set PURE &/or ELEMENTAL as
+// appropriate.
+void ScopeHandler::AcquireIntrinsicProcedureFlags(Symbol &symbol) {
+  symbol.attrs().set(Attr::INTRINSIC);
+  switch (context().intrinsics().GetIntrinsicClass(symbol.name().ToString())) {
+  case evaluate::IntrinsicClass::elementalFunction:
+  case evaluate::IntrinsicClass::elementalSubroutine:
+    symbol.attrs().set(Attr::ELEMENTAL);
+    symbol.attrs().set(Attr::PURE);
+    break;
+  case evaluate::IntrinsicClass::impureSubroutine:
+    break;
+  default:
+    symbol.attrs().set(Attr::PURE);
+  }
+}
+
 const DeclTypeSpec *ScopeHandler::GetImplicitType(
     Symbol &symbol, const Scope &scope) {
   const auto *type{implicitRulesMap_->at(&scope).GetType(symbol.name())};
@@ -3461,14 +3480,14 @@
 bool DeclarationVisitor::Pre(const parser::IntrinsicStmt &x) {
   HandleAttributeStmt(Attr::INTRINSIC, x.v);
   for (const auto &name : x.v) {
-    auto *symbol{FindSymbol(name)};
-    if (!ConvertToProcEntity(*symbol)) {
+    auto &symbol{DEREF(FindSymbol(name))};
+    if (!ConvertToProcEntity(symbol)) {
       SayWithDecl(
-          name, *symbol, "INTRINSIC attribute not allowed on '%s'"_err_en_US);
-    } else if (symbol->attrs().test(Attr::EXTERNAL)) { // C840
-      Say(symbol->name(),
+          name, symbol, "INTRINSIC attribute not allowed on '%s'"_err_en_US);
+    } else if (symbol.attrs().test(Attr::EXTERNAL)) { // C840
+      Say(symbol.name(),
           "Symbol '%s' cannot have both EXTERNAL and INTRINSIC attributes"_err_en_US,
-          symbol->name());
+          symbol.name());
     }
   }
   return false;
@@ -4692,10 +4711,14 @@
     // are acceptable as procedure interfaces.
     Symbol &symbol{
         MakeSymbol(InclusiveScope(), name.source, Attrs{Attr::INTRINSIC})};
+    symbol.set_details(ProcEntityDetails{});
+    symbol.set(Symbol::Flag::Function);
     if (interface->IsElemental()) {
       symbol.attrs().set(Attr::ELEMENTAL);
     }
-    symbol.set_details(ProcEntityDetails{});
+    if (interface->IsPure()) {
+      symbol.attrs().set(Attr::PURE);
+    }
     Resolve(name, symbol);
     return true;
   } else {
@@ -5971,9 +5994,9 @@
     bool convertedToProcEntity{ConvertToProcEntity(*symbol)};
     if (convertedToProcEntity && !symbol->attrs().test(Attr::EXTERNAL) &&
         IsIntrinsic(symbol->name(), flag) && !IsDummy(*symbol)) {
-      symbol->attrs().set(Attr::INTRINSIC);
       // 8.2(3): ignore type from intrinsic in type-declaration-stmt
       symbol->get<ProcEntityDetails>().set_interface(ProcInterface{});
+      AcquireIntrinsicProcedureFlags(*symbol);
     }
     if (!SetProcFlag(name, *symbol, flag)) {
       return; // reported error
@@ -6058,9 +6081,14 @@
     if (flag == Symbol::Flag::Function) {
       ApplyImplicitRules(symbol);
     }
+    if (symbol.attrs().test(Attr::INTRINSIC)) {
+      AcquireIntrinsicProcedureFlags(symbol);
+    }
   } else if (symbol.GetType() && flag == Symbol::Flag::Subroutine) {
     SayWithDecl(
         name, symbol, "Cannot call function '%s' like a subroutine"_err_en_US);
+  } else if (symbol.attrs().test(Attr::INTRINSIC)) {
+    AcquireIntrinsicProcedureFlags(symbol);
   }
   return true;
 }
diff --git a/flang/test/Semantics/call11.f90 b/flang/test/Semantics/call11.f90
--- a/flang/test/Semantics/call11.f90
+++ b/flang/test/Semantics/call11.f90
@@ -80,4 +80,18 @@
     end forall
   end subroutine
 
+  subroutine test4(ch)
+    type :: t
+      real, allocatable :: x
+    end type
+    type(t) :: a(1), b(1)
+    character(*), intent(in) :: ch
+    allocate (b(1)%x)
+    ! Intrinsic functions and a couple subroutines are pure; do not emit errors
+    do concurrent (j=1:1)
+      b(j)%x = cos(1.) + len(ch)
+      call move_alloc(from=b(j)%x, to=a(j)%x)
+    end do
+  end subroutine
+
 end module
diff --git a/flang/test/Semantics/doconcurrent01.f90 b/flang/test/Semantics/doconcurrent01.f90
--- a/flang/test/Semantics/doconcurrent01.f90
+++ b/flang/test/Semantics/doconcurrent01.f90
@@ -164,28 +164,20 @@
   end do
 
 ! Call to MOVE_ALLOC of a coarray outside a DO CONCURRENT.  This is OK.
-call move_alloc(ca, cb)
-
-! Note that the errors below relating to MOVE_ALLOC() bing impure are bogus.  
-! They're the result of the fact that access to the move_alloc() instrinsic 
-! is not yet possible.
+  call move_alloc(ca, cb)
 
+! Call to MOVE_ALLOC with non-coarray arguments in a DO CONCURRENT.  This is OK.
   allocate(aa)
   do concurrent (i = 1:10)
-!ERROR: Call to an impure procedure is not allowed in DO CONCURRENT
     call move_alloc(aa, ab)
   end do
 
-! Call to MOVE_ALLOC with non-coarray arguments in a DO CONCURRENT.  This is OK.
-
   do concurrent (i = 1:10)
-!ERROR: Call to an impure procedure is not allowed in DO CONCURRENT
 !ERROR: An image control statement is not allowed in DO CONCURRENT
     call move_alloc(ca, cb)
   end do
 
   do concurrent (i = 1:10)
-!ERROR: Call to an impure procedure is not allowed in DO CONCURRENT
 !ERROR: An image control statement is not allowed in DO CONCURRENT
     call move_alloc(pvar%type1_field%coarray_type0_field, qvar%type1_field%coarray_type0_field)
   end do
diff --git a/flang/test/Semantics/omp-symbol08.f90 b/flang/test/Semantics/omp-symbol08.f90
--- a/flang/test/Semantics/omp-symbol08.f90
+++ b/flang/test/Semantics/omp-symbol08.f90
@@ -139,7 +139,7 @@
 !$omp parallel do  reduction(+:sum)
   !DEF: /dotprod/Block1/Block1/Block1/Block1/i (OmpPrivate, OmpPreDetermined) HostAssoc INTEGER(4)
   !REF: /dotprod/Block1/Block1/Block1/i0
-  !DEF: /dotprod/min INTRINSIC (Function) ProcEntity
+  !DEF: /dotprod/min ELEMENTAL, INTRINSIC, PURE (Function) ProcEntity
   !REF: /dotprod/block_size
   !REF: /dotprod/n
   do i=i0,min(i0+block_size, n)
diff --git a/flang/test/Semantics/procinterface01.f90 b/flang/test/Semantics/procinterface01.f90
--- a/flang/test/Semantics/procinterface01.f90
+++ b/flang/test/Semantics/procinterface01.f90
@@ -53,13 +53,13 @@
   !DEF: /module1/derived1/p5 NOPASS, POINTER (Function) ProcEntity COMPLEX(4)
   !DEF: /module1/nested4 PUBLIC (Function) Subprogram COMPLEX(4)
   procedure(complex), pointer, nopass :: p5 => nested4
-  !DEF: /module1/sin ELEMENTAL, INTRINSIC, PUBLIC ProcEntity
-  !DEF: /module1/derived1/p6 NOPASS, POINTER ProcEntity
+  !DEF: /module1/sin ELEMENTAL, INTRINSIC, PUBLIC, PURE (Function) ProcEntity
+  !DEF: /module1/derived1/p6 NOPASS, POINTER (Function) ProcEntity
   !REF: /module1/nested1
   procedure(sin), pointer, nopass :: p6 => nested1
   !REF: /module1/sin
-  !DEF: /module1/derived1/p7 NOPASS, POINTER ProcEntity
-  !DEF: /module1/cos ELEMENTAL, INTRINSIC, PUBLIC ProcEntity
+  !DEF: /module1/derived1/p7 NOPASS, POINTER (Function) ProcEntity
+  !DEF: /module1/cos ELEMENTAL, INTRINSIC, PUBLIC, PURE (Function) ProcEntity
   procedure(sin), pointer, nopass :: p7 => cos
   !REF: /module1/tan
   !DEF: /module1/derived1/p8 NOPASS, POINTER (Function) ProcEntity CHARACTER(1_4,1)
@@ -105,7 +105,7 @@
   !REF: /module1/nested4/x
   real, intent(in) :: x
   !DEF: /module1/nested4/nested4 ObjectEntity COMPLEX(4)
-  !DEF: /module1/nested4/cmplx INTRINSIC (Function) ProcEntity
+  !DEF: /module1/nested4/cmplx ELEMENTAL, INTRINSIC, PURE (Function) ProcEntity
   !REF: /module1/nested4/x
   nested4 = cmplx(x+4., 6.)
  end function nested4
diff --git a/flang/test/Semantics/symbol13.f90 b/flang/test/Semantics/symbol13.f90
--- a/flang/test/Semantics/symbol13.f90
+++ b/flang/test/Semantics/symbol13.f90
@@ -10,7 +10,7 @@
  !REF: /f1/n
  !REF: /f1/x1
  !REF: /f1/x2
- !DEF: /f1/len INTRINSIC (Function) ProcEntity
+ !DEF: /f1/len ELEMENTAL, INTRINSIC, PURE (Function) ProcEntity
  character*(n), intent(in) :: x1, x2*(len(x1)+1)
  !DEF: /f1/t DerivedType
  type :: t
diff --git a/flang/test/Semantics/symbol14.f90 b/flang/test/Semantics/symbol14.f90
--- a/flang/test/Semantics/symbol14.f90
+++ b/flang/test/Semantics/symbol14.f90
@@ -17,7 +17,7 @@
   !REF: /MainProgram1/t1/k
   real :: b(k)
   !DEF: /MainProgram1/t2/c ObjectEntity REAL(4)
-  !DEF: /MainProgram1/size INTRINSIC (Function) ProcEntity
+  !DEF: /MainProgram1/size INTRINSIC, PURE (Function) ProcEntity
   !REF: /MainProgram1/t1/a
   real :: c(size(a))
   !REF: /MainProgram1/t1
diff --git a/flang/test/Semantics/symbol15.f90 b/flang/test/Semantics/symbol15.f90
--- a/flang/test/Semantics/symbol15.f90
+++ b/flang/test/Semantics/symbol15.f90
@@ -12,7 +12,7 @@
  !DEF: /m/op1 POINTER, PUBLIC ObjectEntity REAL(4)
  real, pointer :: op1
  !DEF: /m/op2 POINTER, PUBLIC ObjectEntity REAL(4)
- !DEF: /m/null INTRINSIC, PUBLIC (Function) ProcEntity
+ !DEF: /m/null INTRINSIC, PUBLIC, PURE (Function) ProcEntity
  real, pointer :: op2 => null()
  !DEF: /m/op3 POINTER, PUBLIC ObjectEntity REAL(4)
  !DEF: /m/x PUBLIC, TARGET ObjectEntity REAL(4)
diff --git a/flang/test/Semantics/symbol17.f90 b/flang/test/Semantics/symbol17.f90
--- a/flang/test/Semantics/symbol17.f90
+++ b/flang/test/Semantics/symbol17.f90
@@ -70,7 +70,7 @@
  q1%n = 1
 end subroutine
 !DEF: /f2/fwdpdt DerivedType
-!DEF: /f2/kind INTRINSIC (Function) ProcEntity
+!DEF: /f2/kind INTRINSIC, PURE (Function) ProcEntity
 !DEF: /f2 (Function) Subprogram TYPE(fwdpdt(k=4_4))
 !DEF: /f2/n (Implicit) ObjectEntity INTEGER(4)
 type(fwdpdt(kind(0))) function f2(n)
@@ -92,7 +92,7 @@
 !DEF: /s2/q1 (Implicit) ObjectEntity TYPE(fwdpdt(k=4_4))
 subroutine s2 (q1)
  !DEF: /s2/fwdpdt DerivedType
- !DEF: /s2/kind INTRINSIC (Function) ProcEntity
+ !DEF: /s2/kind INTRINSIC, PURE (Function) ProcEntity
  implicit type(fwdpdt(kind(0)))(q)
  !REF: /s2/fwdpdt
  !DEF: /s2/fwdpdt/k TypeParam INTEGER(4)
diff --git a/flang/test/Semantics/symbol18.f90 b/flang/test/Semantics/symbol18.f90
--- a/flang/test/Semantics/symbol18.f90
+++ b/flang/test/Semantics/symbol18.f90
@@ -4,14 +4,14 @@
 
 !DEF: /p1 MainProgram
 program p1
- !DEF: /p1/cos INTRINSIC (Function) ProcEntity
+ !DEF: /p1/cos ELEMENTAL, INTRINSIC, PURE (Function) ProcEntity
  integer cos
  !DEF: /p1/y (Implicit) ObjectEntity REAL(4)
  !REF: /p1/cos
  !DEF: /p1/x (Implicit) ObjectEntity REAL(4)
  y = cos(x)
  !REF: /p1/y
- !DEF: /p1/sin INTRINSIC (Function) ProcEntity
+ !DEF: /p1/sin ELEMENTAL, INTRINSIC, PURE (Function) ProcEntity
  !REF: /p1/x
  y = sin(x)
  !REF: /p1/y
diff --git a/flang/test/Semantics/symbol19.f90 b/flang/test/Semantics/symbol19.f90
--- a/flang/test/Semantics/symbol19.f90
+++ b/flang/test/Semantics/symbol19.f90
@@ -18,7 +18,7 @@
 !DEF: /expect_intrinsic (Subroutine) Subprogram
 subroutine expect_intrinsic
  !DEF: /expect_intrinsic/y (Implicit) ObjectEntity REAL(4)
- !DEF: /expect_intrinsic/acos INTRINSIC (Function) ProcEntity
+ !DEF: /expect_intrinsic/acos ELEMENTAL, INTRINSIC, PURE (Function) ProcEntity
  !DEF: /expect_intrinsic/x (Implicit) ObjectEntity REAL(4)
  y = acos(x)
  !DEF: /expect_intrinsic/system_clock INTRINSIC (Subroutine) ProcEntity