diff --git a/spring-core/src/main/java/org/springframework/core/annotation/AnnotatedMethod.java b/spring-core/src/main/java/org/springframework/core/annotation/AnnotatedMethod.java
index ed9ed52530..519133a623 100644
--- a/spring-core/src/main/java/org/springframework/core/annotation/AnnotatedMethod.java
+++ b/spring-core/src/main/java/org/springframework/core/annotation/AnnotatedMethod.java
@@ -18,6 +18,7 @@ package org.springframework.core.annotation;
 
 import java.lang.annotation.Annotation;
 import java.lang.reflect.Method;
+import java.lang.reflect.Modifier;
 import java.util.ArrayList;
 import java.util.Arrays;
 import java.util.List;
@@ -38,6 +39,7 @@ import org.springframework.util.StringUtils;
  * interface-declared parameter annotations from the concrete target method.
  *
  * @author Juergen Hoeller
+ * @author Sam Brannen
  * @since 6.1
  * @see #getMethodAnnotation(Class)
  * @see #getMethodParameters()
@@ -181,7 +183,7 @@ public class AnnotatedMethod {
 					clazz = null;
 				}
 				if (clazz != null) {
-					for (Method candidate : clazz.getMethods()) {
+					for (Method candidate : clazz.getDeclaredMethods()) {
 						if (isOverrideFor(candidate)) {
 							parameterAnnotations.add(candidate.getParameterAnnotations());
 						}
@@ -194,8 +196,9 @@ public class AnnotatedMethod {
 	}
 
 	private boolean isOverrideFor(Method candidate) {
-		if (!candidate.getName().equals(this.method.getName()) ||
-				candidate.getParameterCount() != this.method.getParameterCount()) {
+		if (Modifier.isPrivate(candidate.getModifiers()) ||
+				!candidate.getName().equals(this.method.getName()) ||
+				(candidate.getParameterCount() != this.method.getParameterCount())) {
 			return false;
 		}
 		Class<?>[] paramTypes = this.method.getParameterTypes();
diff --git a/spring-core/src/test/java/org/springframework/core/annotation/AnnotatedMethodTests.java b/spring-core/src/test/java/org/springframework/core/annotation/AnnotatedMethodTests.java
index 1118239d61..c2c073e624 100644
--- a/spring-core/src/test/java/org/springframework/core/annotation/AnnotatedMethodTests.java
+++ b/spring-core/src/test/java/org/springframework/core/annotation/AnnotatedMethodTests.java
@@ -19,12 +19,15 @@ package org.springframework.core.annotation;
 import java.lang.annotation.Retention;
 import java.lang.annotation.RetentionPolicy;
 import java.lang.reflect.Method;
+import java.lang.reflect.Modifier;
 
 import org.junit.jupiter.api.Test;
 
 import org.springframework.core.MethodParameter;
-import org.springframework.util.ClassUtils;
+import org.springframework.util.ReflectionUtils;
 
+import static java.util.Arrays.stream;
+import static java.util.stream.Collectors.joining;
 import static org.assertj.core.api.Assertions.assertThat;
 
 /**
@@ -55,6 +58,12 @@ class AnnotatedMethodTests {
 
 	@Test
 	void shouldFindAnnotationOnMethodParameterInGenericAbstractSuperclass() {
+		// Prerequisites for gh-35349
+		Method abstractMethod = ReflectionUtils.findMethod(GenericAbstractSuperclass.class, "processTwo", Object.class);
+		assertThat(abstractMethod).isNotNull();
+		assertThat(Modifier.isAbstract(abstractMethod.getModifiers())).as("abstract").isTrue();
+		assertThat(Modifier.isPublic(abstractMethod.getModifiers())).as("public").isFalse();
+
 		Method processTwo = getMethod("processTwo", String.class);
 
 		AnnotatedMethod annotatedMethod = new AnnotatedMethod(processTwo);
@@ -78,7 +87,14 @@ class AnnotatedMethodTests {
 
 
 	private static Method getMethod(String name, Class<?>...parameterTypes) {
-		return ClassUtils.getMethod(GenericInterfaceImpl.class, name, parameterTypes);
+		Class<?> clazz = GenericInterfaceImpl.class;
+		Method method = ReflectionUtils.findMethod(clazz, name, parameterTypes);
+		if (method == null) {
+			String parameterNames = stream(parameterTypes).map(Class::getName).collect(joining(", "));
+			throw new IllegalStateException("Expected method not found: %s#%s(%s)"
+					.formatted(clazz.getSimpleName(), name, parameterNames));
+		}
+		return method;
 	}
 
 
@@ -103,13 +119,14 @@ class AnnotatedMethodTests {
 		}
 
 		@Handler
-		public abstract void processTwo(@Param C value);
+		// Intentionally NOT public
+		abstract void processTwo(@Param C value);
 	}
 
 	static class GenericInterfaceImpl extends GenericAbstractSuperclass<String> {
 
 		@Override
-		public void processTwo(String value) {
+		void processTwo(String value) {
 		}
 	}