Porous shape memory alloys (SMAs) are a relatively new group of materials that are of interest because of their potential use in the design of damping and shock mitigation systems. Benefits of the material include reduced weight, high level of energy absorption through phase transformation and possible increased energy absorption through wave scattering due to porosity. Essential to the use of these materials is an understanding of the structural and shock absorbing response of the material. Constitutive models that accurately represent these characteristics are necessary. The emphasis of this research is to develop a computational methodology that will bridge the mesostructural and macrostructural features of porous SMAs. The first step in the process involves the detailed characterization of the relevant mesostructure, i.e., information about pore shape, size, volume fraction and distribution. This representative characterization can be used to produce realistic image-based finite element models. Because the resultant models have large degrees of freedom they cannot be employed to analyze large-scale structural problems. However, simply designed boundary value problems such as the dynamic uniaxial compressive loading of a bar can be used as benchmarks for the verification of phenomenological macro-constitutive models, or models that are derived using averaging methods such as the Mori-Tanaka method or the self-consistent method. In this study, an attempt is made to analyze numerically porous SMA behavior under dynamic conditions based on the representative mesostructural features. Preliminary results are obtained for selected pore volume fractions and distinct trends in material behavior are observed.