We describe experimental and theoretical studies of the buckling mechanics in silicon nanowires (SiNWs) on elastomeric substrates. The system involves randomly oriented SiNWs grown using established procedures on silicon wafers, and then transferred and organized into aligned arrays on prestrained slabs of poly(dimethylsiloxane) (PDMS). Releasing the prestrain leads to nonlinear mechanical buckling processes that transform the initially linear SiNWs into sinusoidal (i.e., "wavy") shapes. The displacements associated with these waves lie in the plane of the substrate, unlike previously observed behavior in analogous systems of silicon nanoribbons and carbon nanotubes where motion occurs out-of-plane. Theoretical analysis indicates that the energy associated with this in-plane buckling is slightly lower than the out-of-plane case for the geometries and mechanical properties that characterize the SiNWs. An accurate measurement of the Young's modulus of individual SiNWs, between approximately 170 and approximately 110 GPa for the range of wires examined here, emerges from comparison of theoretical analysis to experimental observations. A simple strain gauge built using SiNWs in these wavy geometries demonstrates one area of potential application.