This paper presents numerical simulation strategies for stretchable silicon integrated circuits that use stiff thin film on elastomeric substrates. Detailed numerical simulation studies reveal the key underlying aspects of these systems. The results indicate, as an example, optimized mechanics and materials for circuits that exhibit maximum principal strains less than 0.2% even for applied strains of up to ~90%. Simple circuits, including CMOS inverters provide an example that validates these designs. The results suggest practical routes to high performance electronics with linear elastic responses to large strain deformations, suitable for diverse applications that are not readily addressed with conventional wafer-based technologies.