diff --git a/loopstructural/gui/modelling/steps/checks.py b/loopstructural/gui/modelling/steps/checks.py
index b750a5f..627fb9f 100644
--- a/loopstructural/gui/modelling/steps/checks.py
+++ b/loopstructural/gui/modelling/steps/checks.py
@@ -65,13 +65,18 @@ def check_data(data_manager, model_manager=None) -> StepCheck:
 def check_stratigraphy(data_manager, model_manager=None) -> StepCheck:
     """Step 2: the column and the results that come from it."""
     problems, todo = [], []
+    unit_names = data_manager.get_stratigraphic_unit_names()
+    if not unit_names:
+        # The step is optional: a model of faults only has no column
+        todo.append(
+            "Add units to the stratigraphic column. This step is optional if you model "
+            "only faults."
+        )
+        return StepCheck(tuple(problems), tuple(todo))
     if data_manager.get_layer_role(layer_roles.GEOLOGY) is None:
         todo.append("Select the geology layer.")
     if data_manager.get_layer_role(layer_roles.STRUCTURE) is None:
         todo.append("Select the structure layer.")
-    unit_names = data_manager.get_stratigraphic_unit_names()
-    if not unit_names:
-        todo.append("Add units to the stratigraphic column.")
     problems.extend(_out_of_date_messages(data_manager))
 
     contact_units = set(data_manager.get_unique_basal_units())
diff --git a/loopstructural/gui/modelling/steps/export_panel.py b/loopstructural/gui/modelling/steps/export_panel.py
index 3b43905..4897e9a 100644
--- a/loopstructural/gui/modelling/steps/export_panel.py
+++ b/loopstructural/gui/modelling/steps/export_panel.py
@@ -169,9 +169,30 @@ def set_model_solved(self, solved):
         )
         for tab_index in range(self.tabs.count()):
             self.tabs.widget(tab_index).setEnabled(self._model_solved and self._task is None)
+        # A model of faults only has no units: no stratigraphic surfaces, no block model
+        has_units = not solved or self._has_stratigraphic_features()
+        if has_units and not self.surface_strat.isEnabled():
+            self.surface_strat.setChecked(True)
+        self.surface_strat.setEnabled(has_units)
+        if not has_units:
+            self.surface_strat.setChecked(False)
+        self.tabs.setTabEnabled(1, has_units)
+        if not has_units:
+            self.hint.setText("The model has faults only, so the block model is not offered.")
         if self._model_solved:
             self._set_plane_defaults()
 
+    def _has_stratigraphic_features(self):
+        """Return False if every feature of the model is a fault."""
+        manager = self.model_manager
+        if manager is None:
+            return True
+        faults = set(getattr(manager, 'faults', {}) or {}) | set(
+            getattr(manager, 'parametric_faults', {}) or {}
+        )
+        names = [f.name for f in manager.features() if not f.name.startswith('__')]
+        return any(name not in faults for name in names)
+
     def _plane_values(self):
         return tuple(w.value() for w in self.section_origin) + (self.section_size.value(),)
 
diff --git a/loopstructural/main/derived_refresh.py b/loopstructural/main/derived_refresh.py
index 9e74b41..126cc2f 100644
--- a/loopstructural/main/derived_refresh.py
+++ b/loopstructural/main/derived_refresh.py
@@ -31,12 +31,16 @@ def names_to_refresh(data_manager) -> List[str]:
       because the layer is an input of the user.
     - Thickness: only when it is out of date. A thickness that was never
       calculated can be typed, so the build does not calculate it.
+
+    With no units in the column (a model of faults only), nothing comes from
+    the column, so the list is empty.
     """
     derived = data_manager.derived
     names = []
+    if not data_manager.get_stratigraphic_unit_names():
+        return names
     if (
         data_manager.layer_roles.contacts_source == layer_roles.CONTACTS_FROM_GEOLOGY
-        and data_manager.get_stratigraphic_unit_names()
         and data_manager.get_layer_role(layer_roles.GEOLOGY) is not None
         and data_manager.get_layer_role(layer_roles.GEOLOGY_UNIT_FIELD)
         and derived.status(derived_data.BASAL_CONTACTS) != derived_data.CURRENT
diff --git a/loopstructural/main/model_manager.py b/loopstructural/main/model_manager.py
index d7bc1f7..f87199e 100644
--- a/loopstructural/main/model_manager.py
+++ b/loopstructural/main/model_manager.py
@@ -1106,6 +1106,14 @@ def update_foliation_features(self):
         and the basal contacts and structural orientations data.
         This method will automatically add unconformities based on the stratigraphic column.
         """
+        if self.stratigraphic_column is not None:
+            # also for an empty column, so the model does not keep the units
+            # of the last build
+            self.model.stratigraphic_column = self.stratigraphic_column
+        # A model with faults only has no column, or a column with no units
+        if self.stratigraphic_column is None or not self.stratigraphic_column.get_groups():
+            self._emit('foliation_features_updated')
+            return
         stratigraphic_column = {}
         # Take each unit's training value straight from `get_isovalues()`
         # (LoopStructural core), which is what labels the extracted
@@ -1719,18 +1727,19 @@ def model_state(self) -> str:
 
     @property
     def valid(self):
-        valid = True
-        if len(self.groups) == 0:
-            valid = False
-        if len(self.stratigraphy) == 0:
-            valid = False
-        if len(self.faults) > 0:
-            for _fault_name, fault_data in self.faults.items():
-                if 'data' in fault_data and not fault_data['data'].empty:
-                    valid = True
-                else:
-                    valid = False
-        return valid
+        """True if the model has stratigraphy or faults, and each fault trace has data.
+
+        A model with faults only (traces or parametric faults) has no groups
+        and no stratigraphy.
+        """
+        if any(
+            'data' not in fault_data or fault_data['data'].empty
+            for fault_data in self.faults.values()
+        ):
+            return False
+        has_stratigraphy = len(self.groups) > 0 and len(self.stratigraphy) > 0
+        has_faults = len(self.faults) > 0 or len(self.parametric_faults) > 0
+        return has_stratigraphy or has_faults
 
     def update_model(
         self,
diff --git a/tests/qgis/test_parametric_fault.py b/tests/qgis/test_parametric_fault.py
index 3a84b48..f1a0758 100644
--- a/tests/qgis/test_parametric_fault.py
+++ b/tests/qgis/test_parametric_fault.py
@@ -62,6 +62,20 @@ def test_the_fault_is_built_with_constraints(self, manager):
         manager.update_model(notify_observers=False)
         assert 'F1' in _names(manager)
 
+    def test_a_model_of_faults_only_with_an_empty_column(self, manager):
+        column = StratigraphicColumn()
+        column.clear(basement=False)
+        manager.stratigraphic_column = column
+        manager.add_parametric_fault(_spec())
+        manager.update_model(notify_observers=False)
+        manager.update_all_features(notify_observers=False)
+        assert 'F1' in _names(manager)
+        # no stratigraphic feature
+        assert all(name.startswith(('F1', '__')) for name in _names(manager))
+        assert manager.model.stratigraphic_column is column
+        assert manager.valid
+        assert manager.model_state == 'solved'
+
     def test_the_fault_surface_is_where_the_fault_is(self, manager):
         manager.add_parametric_fault(_spec())
         manager.update_model(notify_observers=False)
diff --git a/tests/unit/test_build_plan.py b/tests/unit/test_build_plan.py
index 0743959..357611c 100644
--- a/tests/unit/test_build_plan.py
+++ b/tests/unit/test_build_plan.py
@@ -176,6 +176,13 @@ def test_no_column_calculates_no_contacts(self, dm):
         dm.units = []
         assert names_to_refresh(dm) == []
 
+    def test_no_column_calculates_no_thickness_even_if_out_of_date(self, dm):
+        dm.derived.record(derived_data.BASAL_CONTACTS)
+        dm.derived.record(derived_data.THICKNESS)
+        dm.inputs = {'unit_order': []}
+        dm.units = []
+        assert names_to_refresh(dm) == []
+
     def test_no_geology_layer_calculates_no_contacts(self, dm):
         dm.layer_roles.values[layer_roles.GEOLOGY] = None
         assert names_to_refresh(dm) == []
diff --git a/tests/unit/test_step_checks.py b/tests/unit/test_step_checks.py
index 5f365a5..668fbfa 100644
--- a/tests/unit/test_step_checks.py
+++ b/tests/unit/test_step_checks.py
@@ -119,9 +119,16 @@ def map_layers(self, dm, request):
     def test_an_empty_column_is_not_started(self, dm):
         check = checks.check_stratigraphy(dm)
         assert check.status == Status.NOT_STARTED
-        assert 'Add units to the stratigraphic column.' in check.todo
+        assert any(t.startswith('Add units to the stratigraphic column.') for t in check.todo)
+        assert 'optional' in check.todo[0]
+
+    def test_an_empty_column_does_not_ask_for_layers_or_contacts(self, dm):
+        todo = checks.check_stratigraphy(dm).todo
+        assert len(todo) == 1
+        assert not checks.check_stratigraphy(dm).problems
 
     def test_missing_map_layers_are_a_todo(self, dm):
+        dm.units = ['a']
         todo = checks.check_stratigraphy(dm).todo
         assert 'Select the geology layer.' in todo
         assert 'Select the structure layer.' in todo