This Letter introduces a biaxially stretchable form of single crystalline silicon that consists of two dimensionally buckled, or "wavy", silicon nanomembranes on elastomeric supports. Fabrication procedures for these structures are described, and various aspects of their geometries and responses to uniaxial and biaxial strains along various directions are presented. Analytical models of the mechanics of these systems provide a framework for quantitatively understanding their behavior. These classes of materials might be interesting as a route to high-performance electronics with full, two-dimensional stretchability.