diff --git a/flang/lib/Semantics/check-declarations.cpp b/flang/lib/Semantics/check-declarations.cpp
--- a/flang/lib/Semantics/check-declarations.cpp
+++ b/flang/lib/Semantics/check-declarations.cpp
@@ -83,7 +83,7 @@
       const SourceName &, const Symbol &, const Procedure &, std::size_t);
   bool CheckDefinedAssignment(const Symbol &, const Procedure &);
   bool CheckDefinedAssignmentArg(const Symbol &, const DummyArgument &, int);
-  void CheckSpecificsAreDistinguishable(const Symbol &, const GenericDetails &);
+  void CheckSpecifics(const Symbol &, const GenericDetails &);
   void CheckEquivalenceSet(const EquivalenceSet &);
   void CheckBlockData(const Scope &);
   void CheckGenericOps(const Scope &);
@@ -1346,7 +1346,7 @@
 
 void CheckHelper::CheckGeneric(
     const Symbol &symbol, const GenericDetails &details) {
-  CheckSpecificsAreDistinguishable(symbol, details);
+  CheckSpecifics(symbol, details);
   common::visit(common::visitors{
                     [&](const GenericKind::DefinedIo &io) {
                       CheckDefinedIoProc(symbol, details, io);
@@ -1369,7 +1369,7 @@
 }
 
 // Check that the specifics of this generic are distinguishable from each other
-void CheckHelper::CheckSpecificsAreDistinguishable(
+void CheckHelper::CheckSpecifics(
     const Symbol &generic, const GenericDetails &details) {
   GenericKind kind{details.kind()};
   DistinguishabilityHelper helper{context_};
@@ -1381,6 +1381,23 @@
         msg->Attach(
             specific.name(), "Definition of '%s'"_en_US, specific.name());
       }
+      continue;
+    }
+    if (specific.attrs().test(Attr::INTRINSIC)) {
+      if (auto *msg{messages_.Say(specific.name(),
+              "Specific procedure '%s' of generic interface '%s' may not be INTRINSIC"_err_en_US,
+              specific.name(), generic.name())}) {
+        msg->Attach(generic.name(), "Definition of '%s'"_en_US, generic.name());
+      }
+      continue;
+    }
+    if (IsStmtFunction(specific)) {
+      if (auto *msg{messages_.Say(specific.name(),
+              "Specific procedure '%s' of generic interface '%s' may not be a statement function"_err_en_US,
+              specific.name(), generic.name())}) {
+        msg->Attach(generic.name(), "Definition of '%s'"_en_US, generic.name());
+      }
+      continue;
     }
     if (const Procedure *procedure{Characterize(specific)}) {
       if (procedure->HasExplicitInterface()) {
diff --git a/flang/test/Semantics/generic06.f90 b/flang/test/Semantics/generic06.f90
new file mode 100644
--- /dev/null
+++ b/flang/test/Semantics/generic06.f90
@@ -0,0 +1,20 @@
+! RUN: %python %S/test_errors.py %s %flang_fc1
+module m
+  !ERROR: Specific procedure 'sin' of generic interface 'yintercept' may not be INTRINSIC
+  intrinsic sin
+  interface yIntercept
+    procedure sin
+  end interface
+  !ERROR: Specific procedure 'cos' of generic interface 'xintercept' may not be INTRINSIC
+  intrinsic cos
+  generic :: xIntercept => cos
+end module
+
+subroutine foo
+  interface slope
+    procedure tan
+  end interface
+  !ERROR: Specific procedure 'tan' of generic interface 'slope' may not be a statement function
+  tan(x) = sin(x) / cos(x)
+end subroutine
+