A swellable downhole packer (10) is provided for positioning downhole in a well to seal with the interior surface of a borehole or the interior surface of a downhole tubular. The packer includes a swellable elastomeric sleeve-shaped body (14) positioned over a mandrel (12) for swelling, and a rigid end ring (16,18). An elastomeric anti-extrusion member (20) is spaced axially between the sleeve-shaped body and the rigid end ring, and has a radial thickness adjacent the end ring greater than the radial thickness adjacent the sleeve-shaped body. A swellable elastomeric member (32) is spaced radially between the exterior surface of the mandrel and the elastomeric anti-extrusion member.