diff --git a/ufl/__init__.py b/ufl/__init__.py
index 57884a507..0a48f8359 100644
--- a/ufl/__init__.py
+++ b/ufl/__init__.py
@@ -303,6 +303,7 @@
     SpatialCoordinate,
 )
 from ufl.integral import Integral
+from ufl.integral_domain import DSIntegralDomain, DsIntegralDomain, DxIntegralDomain
 from ufl.matrix import Matrix
 from ufl.measure import Measure, custom_integral_types, integral_types, register_integral_type
 from ufl.objects import (
@@ -463,8 +464,11 @@
     "Coefficients",
     "Cofunction",
     "Constant",
+    "DSIntegralDomain",
     "Dn",
+    "DsIntegralDomain",
     "Dx",
+    "DxIntegralDomain",
     "ExternalOperator",
     "FacetArea",
     "FacetNormal",
diff --git a/ufl/integral_domain.py b/ufl/integral_domain.py
new file mode 100644
index 000000000..ea8138232
--- /dev/null
+++ b/ufl/integral_domain.py
@@ -0,0 +1,85 @@
+"""Integral domains."""
+
+from abc import ABC, abstractmethod
+
+from ufl.cell import AbstractCell
+from ufl.finiteelement import AbstractFiniteElement
+
+
+class AbstractIntegralDomain(ABC):
+    """Abstract base class for integral domain."""
+
+    def __hash__(self) -> int:
+        """Hash."""
+        return hash(self.__repr__())
+
+    @abstractmethod
+    def __repr__(self) -> str:
+        """Representation."""
+
+    @property
+    @abstractmethod
+    def integral_type(self) -> str:
+        """Integral type."""
+
+
+class DxIntegralDomain(AbstractIntegralDomain):
+    """Integral domain for dx."""
+
+    def __init__(self, coordinate_element: AbstractFiniteElement):
+        """Initialise."""
+        self.coordinate_element = coordinate_element
+
+    def __repr__(self) -> str:
+        """Representation."""
+        return f"DxIntegralDomain({self.coordinate_element!r})"
+
+    @property
+    def integral_type(self) -> str:
+        """Integral type."""
+        return "cell"
+
+
+class DsIntegralDomain(AbstractIntegralDomain):
+    """Integral domain for ds."""
+
+    def __init__(self, coordinate_element: AbstractFiniteElement, facet_type: AbstractCell):
+        """Initialise."""
+        self.coordinate_element = coordinate_element
+        self.facet_type = facet_type
+
+    def __repr__(self) -> str:
+        """Representation."""
+        return f"DsIntegralDomain({self.coordinate_element!r}, {self.facet_type!r})"
+
+    @property
+    def integral_type(self) -> str:
+        """Integral type."""
+        return "exterior_facet"
+
+
+class DSIntegralDomain(AbstractIntegralDomain):
+    """Integral domain for dS."""
+
+    def __init__(
+        self,
+        coordinate_element_positive_side: AbstractFiniteElement,
+        coordinate_element_negative_side: AbstractFiniteElement,
+        facet_type: AbstractCell,
+    ):
+        """Initialise."""
+        self.coordinate_element_positive_side = coordinate_element_positive_side
+        self.coordinate_element_negative_side = coordinate_element_negative_side
+        self.facet_type = facet_type
+
+    def __repr__(self) -> str:
+        """Representation."""
+        return (
+            f"DSIntegralDomain({self.coordinate_element_positive_side!r}, "
+            f"{self.coordinate_element_negative_side!r}, {self.facet_type!r})"
+        )
+
+    @property
+    def integral_type(self) -> str:
+        """Integral type."""
+        return "interior_facet"