A shoe sole having improved cushioning characteristics is disclosed. The sole includes a midsole having a top layer of material and a bottom layer of material. In one embodiment, the top layer of material may be harder than the bottom layer of material. A pattern of lugs defining a wave may be formed on the bottom layer of material. The wave may generally be in the shape of sine wave so as to provide improved cushioning characteristics for the sole. An outsole may also be formed on the bottom layer of material and an upper may be connected to the top layer of material, such that a shoe is formed.