diff --git a/clang-tools-extra/clang-tidy/readability/StaticAccessedThroughInstanceCheck.cpp b/clang-tools-extra/clang-tidy/readability/StaticAccessedThroughInstanceCheck.cpp
--- a/clang-tools-extra/clang-tidy/readability/StaticAccessedThroughInstanceCheck.cpp
+++ b/clang-tools-extra/clang-tidy/readability/StaticAccessedThroughInstanceCheck.cpp
@@ -59,7 +59,7 @@
   if (isa<CXXOperatorCallExpr>(BaseExpr))
     return;
 
-  QualType BaseType =
+  const QualType BaseType =
       BaseExpr->getType()->isPointerType()
           ? BaseExpr->getType()->getPointeeType().getUnqualifiedType()
           : BaseExpr->getType().getUnqualifiedType();
@@ -75,6 +75,11 @@
   std::string BaseTypeName =
       BaseType.getAsString(PrintingPolicyWithSuppressedTag);
 
+  // Ignore anonymous structs/classes which will not have an identifier
+  const RecordDecl *RecDecl = BaseType->getAsCXXRecordDecl();
+  if (!RecDecl || RecDecl->getIdentifier() == nullptr)
+    return;
+
   // Do not warn for CUDA built-in variables.
   if (StringRef(BaseTypeName).startswith("__cuda_builtin_"))
     return;
diff --git a/clang-tools-extra/docs/ReleaseNotes.rst b/clang-tools-extra/docs/ReleaseNotes.rst
--- a/clang-tools-extra/docs/ReleaseNotes.rst
+++ b/clang-tools-extra/docs/ReleaseNotes.rst
@@ -255,8 +255,9 @@
   be unnecessarily emitted for template dependent ``if constexpr``.
 
 - Improved :doc:`readability-static-accessed-through-instance
-  <clang-tidy/checks/readability/static-accessed-through-instance>` check to 
-  support unscoped enumerations through instances.
+  <clang-tidy/checks/readability/static-accessed-through-instance>` check to
+  support unscoped enumerations through instances and fixed usage of anonymous
+  structs or classes.
 
 - Fixed a false positive in :doc:`cppcoreguidelines-slicing
   <clang-tidy/checks/cppcoreguidelines/slicing>` check when warning would be
diff --git a/clang-tools-extra/test/clang-tidy/checkers/readability/static-accessed-through-instance.cpp b/clang-tools-extra/test/clang-tidy/checkers/readability/static-accessed-through-instance.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/readability/static-accessed-through-instance.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/readability/static-accessed-through-instance.cpp
@@ -306,3 +306,60 @@
 // CHECK-MESSAGES-NOT: :[[@LINE-1]]:10: warning: static member
 
 } // namespace Bugzilla_48758
+
+// https://github.com/llvm/llvm-project/issues/61736
+namespace llvm_issue_61736
+{
+
+struct {
+  static void f() {}
+} AnonStruct, *AnonStructPointer;
+
+class {
+  public:
+  static void f() {}
+} AnonClass, *AnonClassPointer;
+
+void testAnonymousStructAndClass() {
+  AnonStruct.f();
+  AnonStructPointer->f();
+
+  AnonClass.f();
+  AnonClassPointer->f();
+}
+
+struct Embedded {
+  struct {
+    static void f() {}
+  } static EmbeddedStruct, *EmbeddedStructPointer;
+
+  class {
+    public:
+      static void f() {}
+  } static EmbeddedClass, *EmbeddedClassPointer;
+};
+
+void testEmbeddedAnonymousStructAndClass() {
+  Embedded::EmbeddedStruct.f();
+  Embedded::EmbeddedStructPointer->f();
+
+  Embedded::EmbeddedClass.f();
+  Embedded::EmbeddedClassPointer->f();
+
+  Embedded E;
+  E.EmbeddedStruct.f();
+  // CHECK-MESSAGES: :[[@LINE-1]]:3: warning: static member accessed through instance [readability-static-accessed-through-instance]
+  // CHECK-FIXES: {{^}}  llvm_issue_61736::Embedded::EmbeddedStruct.f();{{$}}
+  E.EmbeddedStructPointer->f();
+  // CHECK-MESSAGES: :[[@LINE-1]]:3: warning: static member accessed through instance [readability-static-accessed-through-instance]
+  // CHECK-FIXES: {{^}}  llvm_issue_61736::Embedded::EmbeddedStructPointer->f();{{$}}
+
+  E.EmbeddedClass.f();
+  // CHECK-MESSAGES: :[[@LINE-1]]:3: warning: static member accessed through instance [readability-static-accessed-through-instance]
+  // CHECK-FIXES: {{^}}  llvm_issue_61736::Embedded::EmbeddedClass.f();{{$}}
+  E.EmbeddedClassPointer->f();
+  // CHECK-MESSAGES: :[[@LINE-1]]:3: warning: static member accessed through instance [readability-static-accessed-through-instance]
+  // CHECK-FIXES: {{^}}  llvm_issue_61736::Embedded::EmbeddedClassPointer->f();{{$}}
+}
+
+} // namespace llvm_issue_61736