An animal toy includes a compressibly elastically deformable hollow thin-walled elastomer core sealingly circumscribing a center, includes an exterior including a first gravure elastomer relief surface and a second surface, includes a wall less than about eight millimeters thick, and includes points on the exterior at varying distances from the center. A fabric cover is affixed to the second surface and has a selected thickness, the ratio of the thickness of the fabric cover to the thickness of the wall being in the range of 1:6 to 1:0.15.