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
@@ -114,6 +114,7 @@
   }
   bool IsResultOkToDiffer(const FunctionResult &);
   void CheckBindC(const Symbol &);
+  void CheckBindCFunctionResult(const Symbol &);
   // Check functions for defined I/O procedures
   void CheckDefinedIoProc(
       const Symbol &, const GenericDetails &, GenericKind::DefinedIo);
@@ -399,6 +400,7 @@
       messages_.Say(
           "A function result may not have the SAVE attribute"_err_en_US);
     }
+    CheckBindCFunctionResult(symbol);
   }
   if (symbol.owner().IsDerivedType() &&
       (symbol.attrs().test(Attr::CONTIGUOUS) &&
@@ -416,6 +418,35 @@
 
 void CheckHelper::CheckCommonBlock(const Symbol &symbol) { CheckBindC(symbol); }
 
+void CheckHelper::CheckBindCFunctionResult(const Symbol &symbol) { // C1553
+  if (!innermostSymbol_ || !IsBindCProcedure(*innermostSymbol_)) {
+    return;
+  }
+  if (IsPointer(symbol) || IsAllocatable(symbol)) {
+    messages_.Say(
+        "BIND(C) function result cannot have ALLOCATABLE or POINTER attribute"_err_en_US);
+  }
+  if (const DeclTypeSpec * type{symbol.GetType()};
+      type && type->category() == DeclTypeSpec::Character) {
+    bool isConstOne{false}; // 18.3.1(1)
+    if (const auto &len{type->characterTypeSpec().length().GetExplicit()}) {
+      if (auto constLen{evaluate::ToInt64(*len)}) {
+        isConstOne = constLen == 1;
+      }
+    }
+    if (!isConstOne) {
+      messages_.Say(
+          "BIND(C) character function result must have length one"_err_en_US);
+    }
+  }
+  if (symbol.Rank() > 0) {
+    messages_.Say("BIND(C) function result must be scalar"_err_en_US);
+  }
+  if (symbol.Corank()) {
+    messages_.Say("BIND(C) function result cannot be a coarray"_err_en_US);
+  }
+}
+
 void CheckHelper::CheckValue(
     const Symbol &symbol, const DerivedTypeSpec *derived) { // C863 - C865
   if (!IsDummy(symbol)) {
diff --git a/flang/test/Semantics/bind-c09.f90 b/flang/test/Semantics/bind-c09.f90
new file mode 100644
--- /dev/null
+++ b/flang/test/Semantics/bind-c09.f90
@@ -0,0 +1,49 @@
+! RUN: %python %S/test_errors.py %s %flang_fc1
+! Check for C1553 and 18.3.4(1)
+
+function func1() result(res) bind(c)
+  ! ERROR: BIND(C) function result cannot have ALLOCATABLE or POINTER attribute
+  integer, pointer :: res
+end
+
+function func2() result(res) bind(c)
+  ! ERROR: BIND(C) function result cannot have ALLOCATABLE or POINTER attribute
+  integer, allocatable :: res
+end
+
+function func3() result(res) bind(c)
+  ! ERROR: BIND(C) function result must be scalar
+  integer :: res(2)
+end
+
+function func4() result(res) bind(c)
+  ! ERROR: BIND(C) character function result must have length one
+  character(*) :: res
+end
+
+function func5(n) result(res) bind(c)
+  integer :: n
+  ! ERROR: BIND(C) character function result must have length one
+  character(n) :: res
+end
+
+function func6() result(res) bind(c)
+  ! ERROR: BIND(C) character function result must have length one
+  character(2) :: res
+end
+
+function func7() result(res) bind(c)
+  integer, parameter :: n = 1
+  character(n) :: res ! OK
+end
+
+function func8() result(res) bind(c)
+  ! ERROR: BIND(C) function result cannot have ALLOCATABLE or POINTER attribute
+  ! ERROR: BIND(C) character function result must have length one
+  character(:), pointer :: res
+end
+
+function func9() result(res) bind(c)
+  ! ERROR: BIND(C) function result cannot be a coarray
+  integer :: res[10, *]
+end