The primary objective of this investigation is the optimum design of lightweight foam material systems for controlled energy absorption under blast impact. The ultimate goal of these systems is to increase the safety and integrity of occupants and critical components in structural systems such as automotive vehicles, buildings, ships, and aircrafts. Although outstanding results have been achieved with the use of foams in blast protective systems, current design practices rely on trial and error as there is an absence of a systematic design method. While the governing equations are known for a variety of physical phenomena in appropriate length scales, there are no suitable methodologies to accomplish the aforementioned objectives. A promising approach to systematically design the material's microstructure is the use of structural optimization methods. This investigation presents an appropriate design methodology to optimally design foam material systems for blast mitigation. The objective function is expressed in terms of acceleration. Macroscopic effective material properties are used to drive the nonlinear analysis of the elasto-plastic material under time-dependent loading conditions. Gradient-based optimization methods are used to obtain the final density distribution of the foam material system. The application of this approach is shown through a two-dimensional optimization problem.