A shoe sole is described that provides both cushioning and stability. The sole has a plurality of layers, including a transition layer which allows relative motion between the layers adjacent to the transition layer. The relative motion between the layers of the sole reduces the impact of horizontal shear stresses on the wearer's feet and ankles. One such transition layer includes pliable material and deformable holes within the pliable material. Another transition layer includes at least two rigid plates held together by less rigid grommets or sidewalls. The transition layer may be disposed beneath the entire shoe or only portions of the shoe, with either a more conventional sole structure or rigid support members completing the sole.