diff --git a/django/contrib/gis/db/backends/spatialite/operations.py b/django/contrib/gis/db/backends/spatialite/operations.py
index 1413f2227b4..6dc5048b1b7 100644
--- a/django/contrib/gis/db/backends/spatialite/operations.py
+++ b/django/contrib/gis/db/backends/spatialite/operations.py
@@ -80,19 +80,23 @@ class SpatiaLiteOperations(BaseSpatialOperations, DatabaseOperations):
         'distance_lte': SpatialOperator(func='Distance', op='<='),
     }
 
-    function_names = {
-        'Length': 'ST_Length',
-        'Reverse': 'ST_Reverse',
-        'Scale': 'ScaleCoords',
-        'Translate': 'ST_Translate',
-        'Union': 'ST_Union',
-    }
+    @cached_property
+    def function_names(self):
+        return {
+            'Length': 'ST_Length',
+            'Reverse': 'ST_Reverse',
+            'Scale': 'ScaleCoords',
+            'Translate': 'ST_Translate' if self.spatial_version >= (3, 1, 0) else 'ShiftCoords',
+            'Union': 'ST_Union',
+        }
 
     @cached_property
     def unsupported_functions(self):
         unsupported = {'BoundingCircle', 'ForceRHR', 'GeoHash', 'MemSize'}
+        if self.spatial_version < (3, 1, 0):
+            unsupported.add('SnapToGrid')
         if self.spatial_version < (4, 0, 0):
-            unsupported.add('Reverse')
+            unsupported.update({'Perimeter', 'Reverse'})
         return unsupported
 
     @cached_property
diff --git a/django/contrib/gis/db/models/functions.py b/django/contrib/gis/db/models/functions.py
index 4902520b86c..792edac929a 100644
--- a/django/contrib/gis/db/models/functions.py
+++ b/django/contrib/gis/db/models/functions.py
@@ -403,9 +403,12 @@ class Transform(GeoFunc):
 
 class Translate(Scale):
     def as_sqlite(self, compiler, connection):
-        # Always provide the z parameter
-        if len(self.source_expressions) < 4:
+        func_name = connection.ops.spatial_function_name(self.name)
+        if func_name == 'ST_Translate' and len(self.source_expressions) < 4:
+            # Always provide the z parameter for ST_Translate (Spatialite >= 3.1)
             self.source_expressions.append(Value(0))
+        elif func_name == 'ShiftCoords' and len(self.source_expressions) > 3:
+            raise ValueError("This version of Spatialite doesn't support 3D")
         return super(Translate, self).as_sqlite(compiler, connection)
 
 
diff --git a/tests/gis_tests/geoapp/test_functions.py b/tests/gis_tests/geoapp/test_functions.py
index b17a1a2fc08..edef090c5be 100644
--- a/tests/gis_tests/geoapp/test_functions.py
+++ b/tests/gis_tests/geoapp/test_functions.py
@@ -2,6 +2,7 @@ from __future__ import unicode_literals
 
 import re
 from decimal import Decimal
+from unittest import skipUnless
 
 from django.contrib.gis.db.models import functions
 from django.contrib.gis.geos import HAS_GEOS
@@ -12,7 +13,9 @@ from django.utils import six
 from ..utils import mysql, oracle, postgis, spatialite
 
 if HAS_GEOS:
-    from django.contrib.gis.geos import LineString, Point, Polygon, fromstr
+    from django.contrib.gis.geos import (
+        LineString, Point, Polygon, fromstr, geos_version_info,
+    )
     from .models import Country, City, State, Track
 
 
@@ -382,6 +385,7 @@ class GISFunctionsTests(TestCase):
         )
 
     @skipUnlessDBFeature("has_SymDifference_function")
+    @skipUnless(HAS_GEOS and geos_version_info()['version'] >= '3.3.0', "GEOS >= 3.3 required")
     def test_sym_difference(self):
         geom = Point(5, 23, srid=4326)
         qs = Country.objects.annotate(sym_difference=functions.SymDifference('mpoly', geom))