diff --git a/clang/docs/ReleaseNotes.rst b/clang/docs/ReleaseNotes.rst
index 6b396e7ba63f3..d19cc041b5082 100644
--- a/clang/docs/ReleaseNotes.rst
+++ b/clang/docs/ReleaseNotes.rst
@@ -222,6 +222,8 @@ C23 Feature Support
   the same translation unit but from different types.
 - ``-MG`` now silences the "file not found" errors with ``#embed`` when
   scanning for dependencies and encountering an unknown file. #GH165632
+- Allow NaN in constant expression evaluation to maintain consistency with
+  GCC in behavior, even though it's an undefined behavior. #GH161806
 
 Non-comprehensive list of changes in this release
 -------------------------------------------------
diff --git a/clang/lib/AST/Decl.cpp b/clang/lib/AST/Decl.cpp
index 8579e51e45697..53ed180f377a1 100644
--- a/clang/lib/AST/Decl.cpp
+++ b/clang/lib/AST/Decl.cpp
@@ -2605,11 +2605,18 @@ APValue *VarDecl::evaluateValueImpl(SmallVectorImpl<PartialDiagnosticAt> &Notes,
   // a constant initializer if we produced notes. In that case, we can't keep
   // the result, because it may only be correct under the assumption that the
   // initializer is a constant context.
-  if (IsConstantInitialization &&
-      (Ctx.getLangOpts().CPlusPlus ||
-       (isConstexpr() && Ctx.getLangOpts().C23)) &&
-      !Notes.empty())
-    Result = false;
+  if (IsConstantInitialization && !Notes.empty()) {
+    if (getLangOpts().CPlusPlus)
+      Result = false;
+
+    // Even though hitting an NaN during constant evaluation is an undefined
+    // behavior, we expect to maintain consistency with GCC in behavior, that
+    // is, allow NaN to appear in constant evaluation.
+    bool isNaN =
+        Eval->Evaluated.isFloat() && Eval->Evaluated.getFloat().isNaN();
+    if (getLangOpts().C23 && !isNaN)
+      Result = false;
+  }
 
   // Ensure the computed APValue is cleaned up later if evaluation succeeded,
   // or that it's empty (so that there's nothing to clean up) if evaluation
@@ -2676,8 +2683,14 @@ bool VarDecl::checkForConstantInitialization(
   assert(!getInit()->isValueDependent());
 
   // Evaluate the initializer to check whether it's a constant expression.
-  Eval->HasConstantInitialization =
-      evaluateValueImpl(Notes, true) && Notes.empty();
+  auto *Result = evaluateValueImpl(Notes, true);
+
+  // Even though hitting an NaN during constant evaluation is an undefined
+  // behavior, we expect to maintain consistency with GCC in behavior, that is,
+  // allow NaN to appear in constant evaluation.
+  bool isNaN = Result && Result->isFloat() && Result->getFloat().isNaN();
+  bool AllowNaN = getLangOpts().C23 && isNaN;
+  Eval->HasConstantInitialization = Result && (Notes.empty() || AllowNaN);
 
   // If evaluation as a constant initializer failed, allow re-evaluation as a
   // non-constant initializer if we later find we want the value.
diff --git a/clang/lib/AST/ExprConstant.cpp b/clang/lib/AST/ExprConstant.cpp
index 972d9fe3b5e4f..bd62fbb2edce4 100644
--- a/clang/lib/AST/ExprConstant.cpp
+++ b/clang/lib/AST/ExprConstant.cpp
@@ -3056,7 +3056,8 @@ static bool handleFloatFloatBinOp(EvalInfo &Info, const BinaryOperator *E,
   // FIXME: C++ rules require us to not conform to IEEE 754 here.
   if (LHS.isNaN()) {
     Info.CCEDiag(E, diag::note_constexpr_float_arithmetic) << LHS.isNaN();
-    return Info.noteUndefinedBehavior();
+    bool keepEvaluatingAfterUB = Info.noteUndefinedBehavior();
+    return Info.Ctx.getLangOpts().C23 || keepEvaluatingAfterUB;
   }
 
   return checkFloatingPointResult(Info, E, St);
@@ -19707,7 +19708,8 @@ bool Expr::EvaluateAsInitializer(APValue &Value, const ASTContext &Ctx,
 
   EvalInfo Info(Ctx, EStatus,
                 (IsConstantInitialization &&
-                 (Ctx.getLangOpts().CPlusPlus || Ctx.getLangOpts().C23))
+                 (Ctx.getLangOpts().CPlusPlus ||
+                  (Ctx.getLangOpts().C23 && VD->isConstexpr())))
                     ? EvaluationMode::ConstantExpression
                     : EvaluationMode::ConstantFold);
   Info.setEvaluatingDecl(VD, Value);
diff --git a/clang/test/AST/const-nan.c b/clang/test/AST/const-nan.c
new file mode 100644
index 0000000000000..c732abac4a90d
--- /dev/null
+++ b/clang/test/AST/const-nan.c
@@ -0,0 +1,32 @@
+// RUN: %clang_cc1 -std=c23 -triple i386-linux %s -fsyntax-only -verify
+// RUN: %clang_cc1 -std=c23 -emit-llvm -triple i386-linux %s -o - | FileCheck %s
+
+// expected-no-diagnostics
+
+// CHECK: @[[CONST:.*]] = private unnamed_addr constant [1 x float] [float 0x7FF8000000000000], align 4
+// CHECK: @[[F_X:.*]] = internal global float 0x7FF8000000000000, align 4
+#pragma STDC FENV_ACCESS ON
+void f(void)
+{
+  // CHECK: %[[V:.*]] = alloca double, align 8
+  // CHECK: %[[W:.*]] = alloca [1 x float], align 4
+  // CHECK: %[[Y:.*]] = alloca float, align 4
+  // CHECK: %[[Z:.*]] = alloca double, align 8
+
+  // CHECK: store double 0x7FF8000000000000, ptr %[[V]], align 8
+  constexpr double v = 0.0/0.0; // does not raise an exception
+
+  // CHECK: call void @llvm.memcpy.p0.p0.i32(ptr align 4 %[[W]], ptr align 4 @[[CONST]], i32 4, i1 false)
+  float w[] = { 0.0f/0.0f }; // raises an exception
+
+  // F_X
+  static float x = 0.0f/0.0f; // does not raise an exception
+
+  // CHECK: %[[DIV:.*]] = call float @llvm.experimental.constrained.fdiv.f32(float 0.000000e+00, float 0.000000e+00, metadata !"round.dynamic", metadata !"fpexcept.strict")
+  // CHECK: store float %[[DIV]], ptr %[[Y]], align 4
+  float y = 0.0f/0.0f; // raises an exception
+
+  // CHECK: %[[DIV1:.*]] = call double @llvm.experimental.constrained.fdiv.f64(double 0.000000e+00, double 0.000000e+00, metadata !"round.dynamic", metadata !"fpexcept.strict")
+  // CHECK: store double %[[DIV1]], ptr %[[Z]], align 8
+  double z = 0.0/0.0; // raises an exception
+}