The present invention provides apparatus and methods for imbedding a durable outer layer of rubber in a second layer of rubber, polyurethane, or like material for use in various applications, including but not limited to shoe soles and tires. As depicted in FIG., the durable outer layer, which in the case of FIG. 4 is a shoe outsole, may comprise a plurality of lugs (2) connected with integral support bridges (3) imbedded in another rubber or rubber-like material (17). Alternatively, the durable outer layer may comprise a plurality of lugs anchored in the second layer of rubber, polyurethane or the like, using anchors, such as ribs or flanges, radiating from the perimeter of each lug.