Shock mounts are crucial components in reducing the transmissibility of a shock or impact, thereby protecting the objective system. Such shock mounts are application-specific and need a redesign for specific uses. This study establishes a transient nonlinear finite element optimization procedure to design a shock mount for withstanding an underwater blast wave. The work showcases the analysis of two design concepts. The first design demonstrates average acceleration transmissibility of 5.51e-3. The second design exploits the phenomenon of reflection of waves at an interface. This design is unique, promising a factor 3.263 lower average transmissibility than the first design which is similar without the metal interface. The study also details the modeling and analysis of both shock mount designs using 2D axisymmetric and 3D transient nonlinear finite element analyses. The results of both these analyses were comparable, making a 2D study efficient and reliable in the analysis and optimization of shock mounts.