diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 7802ef4798659..157b87c93e729 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -245,6 +245,7 @@ Removal of prior version deprecations/changes
 
 Performance improvements
 ~~~~~~~~~~~~~~~~~~~~~~~~
+- :meth:`RangeIndex.append` returns a :class:`RangeIndex` instead of a :class:`Index` when appending values that could continue the :class:`RangeIndex` (:issue:`57467`)
 - :meth:`Series.str.extract` returns a :class:`RangeIndex` columns instead of an :class:`Index` column when possible (:issue:`57542`)
 - Performance improvement in :class:`DataFrame` when ``data`` is a ``dict`` and ``columns`` is specified (:issue:`24368`)
 - Performance improvement in :meth:`DataFrame.join` for sorted but non-unique indexes (:issue:`56941`)
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 09d635b53c482..0781a86e5d57e 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -989,7 +989,10 @@ def _concat(self, indexes: list[Index], name: Hashable) -> Index:
         indexes = [RangeIndex(3), RangeIndex(4, 6)] -> Index([0,1,2,4,5], dtype='int64')
         """
         if not all(isinstance(x, RangeIndex) for x in indexes):
-            return super()._concat(indexes, name)
+            result = super()._concat(indexes, name)
+            if result.dtype.kind == "i":
+                return self._shallow_copy(result._values)
+            return result
 
         elif len(indexes) == 1:
             return indexes[0]
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index 898548d1cc4dc..8c24ce5d699d5 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -608,6 +608,20 @@ def test_range_index_rsub_by_const(self):
         tm.assert_index_equal(result, expected)
 
 
+def test_append_non_rangeindex_return_rangeindex():
+    ri = RangeIndex(1)
+    result = ri.append(Index([1]))
+    expected = RangeIndex(2)
+    tm.assert_index_equal(result, expected, exact=True)
+
+
+def test_append_non_rangeindex_return_index():
+    ri = RangeIndex(1)
+    result = ri.append(Index([1, 3, 4]))
+    expected = Index([0, 1, 3, 4])
+    tm.assert_index_equal(result, expected, exact=True)
+
+
 def test_reindex_returns_rangeindex():
     ri = RangeIndex(2, name="foo")
     result, result_indexer = ri.reindex([1, 2, 3])