Abstract: A running shoe outsole includes two layers, wherein the two layers are made of one or materials including carbon fiber, carbon nanotubes, glass fibers, or buckypaper. The two layers curve in an upward direction from the ball region to the heel region. The two layers are fixedly attached at the foremost portions of the toe regions. At the arch region, the sides of either the top layer or the bottom layer may be extended to cradle either the top layer or the bottom layer to prevent lateral movement of one layer in relation to the other. The extended sides or brackets guide lengthwise sliding of one layer in relation to the other layer. The top layer forms a sleeve at the arch region where the bottom layer slides therein.