Abstract: A rug is configured from a cover attached to an underlying, non-slip, non-absorbent mat by an interlocking mechanical connection. The interlocking mechanical connection is formed in a first embodiment by hook and loop material of the type sold under the trademark VELCRO, and in a second embodiment by a layer of grit material on the mat, and in a third embodiment by a resinous material which has projections that interlock with the bottom surface of the cover. When it is desired to separate the cover from the mat, the cover is simply pulled and stripped away from the mat so that the cover may be washed in a washing machine and the mat may also be manually washed or otherwise cleaned. If desired, the cover may be replaced with covers of different designs or textures.