diff --git a/lib/checkclass.cpp b/lib/checkclass.cpp
index eb77a3aac..3251e771c 100644
--- a/lib/checkclass.cpp
+++ b/lib/checkclass.cpp
@@ -2214,8 +2214,14 @@ bool CheckClass::checkConstFunc(const Scope *scope, const Function *func, bool&
                 const Variable *var = lastVarTok->variable();
                 if (!var)
                     return false;
-                if (var->isStlType() // assume all std::*::size() and std::*::empty() are const
-                    && (Token::Match(end, "size|empty|cend|crend|cbegin|crbegin|max_size|length|count|capacity|get_allocator|c_str|str ( )") || Token::Match(end, "rfind|copy")))
+                if ((var->isStlType() // assume all std::*::size() and std::*::empty() are const
+                     && (Token::Match(end, "size|empty|cend|crend|cbegin|crbegin|max_size|length|count|capacity|get_allocator|c_str|str ( )") || Token::Match(end, "rfind|copy"))) ||
+
+                    (lastVarTok->valueType() && lastVarTok->valueType()->container &&
+                     ((lastVarTok->valueType()->container->getYield(end->str()) == Library::Container::Yield::START_ITERATOR) ||
+                      (lastVarTok->valueType()->container->getYield(end->str()) == Library::Container::Yield::END_ITERATOR))
+                     && (tok1->previous()->isComparisonOp() ||
+                         (tok1->previous()->isAssignmentOp() && tok1->tokAt(-2)->variable() && Token::Match(tok1->tokAt(-2)->variable()->typeEndToken(), "const_iterator|const_reverse_iterator")))))
                     ;
                 else if (!var->typeScope() || !isConstMemberFunc(var->typeScope(), end))
                     return false;
diff --git a/test/cfg/std.cpp b/test/cfg/std.cpp
index 84e407481..bca35fd38 100644
--- a/test/cfg/std.cpp
+++ b/test/cfg/std.cpp
@@ -3681,3 +3681,46 @@ void stdbind()
     // cppcheck-suppress unreadVariable
     auto f2 = std::bind(stdbind_helper, 10);
 }
+
+class A
+{
+    std::vector<std::string> m_str;
+
+public:
+
+    A() {}
+
+    // cppcheck-suppress functionConst
+    void begin_const_iterator(void)
+    {
+        for (std::vector<std::string>::const_iterator it = m_str.begin(); it != m_str.end(); ++it) {;}
+    }
+    // cppcheck-suppress functionConst
+    void cbegin_const_iterator(void)
+    {
+        for (std::vector<std::string>::const_iterator it = m_str.cbegin(); it != m_str.cend(); ++it) {;}
+    }
+    // cppcheck-suppress functionConst
+    void crbegin_const_iterator(void)
+    {
+        for (std::vector<std::string>::const_reverse_iterator it = m_str.crbegin(); it != m_str.crend(); ++it) {;}
+    }
+    // cppcheck-suppress functionConst
+    void rbegin_const_iterator(void)
+    {
+        for (std::vector<std::string>::const_reverse_iterator it = m_str.rbegin(); it != m_str.rend(); ++it) {;}
+    }
+    // cppcheck-suppress functionConst
+    void cbegin_auto(void)
+    {
+        for (auto it = m_str.cbegin(); it != m_str.cend(); ++it) {;}
+    }
+    void baz_begin_no_const_iterator(void)
+    {
+        for (std::vector<std::string>::iterator it = m_str.begin(); it != m_str.end(); ++it) {;}
+    }
+    void rbegin_no_const_iterator(void)
+    {
+        for (std::vector<std::string>::reverse_iterator it = m_str.rbegin(); it != m_str.rend(); ++it) {;}
+    }
+};
diff --git a/test/testclass.cpp b/test/testclass.cpp
index 4b7beff60..3d0e205b6 100644
--- a/test/testclass.cpp
+++ b/test/testclass.cpp
@@ -53,6 +53,12 @@ private:
                                    "    <dealloc>free</dealloc>\n"
                                    "  </memory>\n"
                                    "  <smart-pointer class-name=\"std::shared_ptr\"/>\n"
+                                   "  <container id=\"stdVector\" startPattern=\"std :: vector &lt;\" itEndPattern=\"&gt; :: const_iterator\">\n"
+                                   "    <access>\n"
+                                   "      <function name=\"begin\" yields=\"start-iterator\"/>\n"
+                                   "      <function name=\"end\" yields=\"end-iterator\"/>\n"
+                                   "    </access>\n"
+                                   "  </container>\n"
                                    "</def>";
             tinyxml2::XMLDocument doc;
             doc.Parse(xmldata, sizeof(xmldata));
@@ -183,6 +189,7 @@ private:
         TEST_CASE(const71); // ticket #10146
         TEST_CASE(const72); // ticket #10520
         TEST_CASE(const73); // ticket #10735
+        TEST_CASE(const74); // ticket #10671
         TEST_CASE(const_handleDefaultParameters);
         TEST_CASE(const_passThisToMemberOfOtherClass);
         TEST_CASE(assigningPointerToPointerIsNotAConstOperation);
@@ -5918,6 +5925,28 @@ private:
         ASSERT_EQUALS("[test.cpp:5] -> [test.cpp:3]: (style, inconclusive) Technically the member function 'S::f' can be const.\n", errout.str());
     }
 
+    void const74() { // #10671
+        checkConst("class A {\n"
+                   "    std::vector<std::string> m_str;\n"
+                   "public:\n"
+                   "    A() {}\n"
+                   "    void bar(void) {\n"
+                   "        for(std::vector<std::string>::const_iterator it = m_str.begin(); it != m_str.end(); ++it) {;}\n"
+                   "    }\n"
+                   "};");
+        ASSERT_EQUALS("[test.cpp:5]: (style, inconclusive) Technically the member function 'A::bar' can be const.\n", errout.str());
+
+        // Don't crash
+        checkConst("struct S {\n"
+                   "    std::vector<T*> v;\n"
+                   "    void f() const;\n"
+                   "};\n"
+                   "void S::f() const {\n"
+                   "    for (std::vector<T*>::const_iterator it = v.begin(), end = v.end(); it != end; ++it) {}\n"
+                   "}\n");
+        ASSERT_EQUALS("", errout.str());
+    }
+
     void const_handleDefaultParameters() {
         checkConst("struct Foo {\n"
                    "    void foo1(int i, int j = 0) {\n"