This study presents a density based topology optimization method with prescribed input displacement boundary condition to design an elastomeric engine mount. The required stiffness values for the rubber mount have different requirements in two different loading directions. Various design analysis cases are performed to provide design guideline for investigating the effects of several design parameters on static stiffness of the elastomer mount. Simulation models are developed using the commercial finite element analysis program, LS-DYNA, to analyze the designs. One commercial elastomeric engine mount is selected as the validation example in this study. The analysis results show the simulated stiffness values agree well with experimental data. The design examples and results provided in this study can serve as the design reference for developing elastomer mounts with desired stiffness.