Most static fault models have the limitation of simulating crustal rigidity variation in one direction only. Improving on these, the model presented here is a static, two-dimensional strike-slip model which generates elastic deformation data in a bi-directionally varying crust. Specifically, the Earth is modeled as a homogeneous elastic surface layer plus a horizontally varying elastic substrata. The cumulative effects of bi-directional rigidity variations on surface deformation data were examined for a number of rigidity profiles. For those rigidity schemes containing a compliant, fault zone, the amplitude of surface data could either be amplified or reduced depending on the rigidity and thickness of the surface layer. For rigidity schemes containing a buried, long, narrow, vertical heterogeneity in the substrata, the surface layer tended to mask or reduce any perturbations to the data caused by the heterogeneity. As has been established for uni-directional models and is affirmed for bi-directionally varying models, rigidity contrasts or heterogeneities in the vicinity of crustal deformation measuring devices will profoundly affect the data taken by these devices.