This repository contains codes I wrote as an undergraduate at Utah State University. I studied the surface deformation patterns generated by geodynamic flow models with different rheological assumptions. The first model is a two-layer viscous flow model of the lithosphere-asthenosphere system with a 'sticky-air' free surface. The second model takes the vertical tractions at the base of the lithosphere from the first model as forcing for the flexure of an elastic beam. I then compared the surface deflection in these two models through time. The differences in the resutling surface deflection and their evolution through time demonstrate 1) a primary limitation of viscous flow models and 2) the importance of incorporating the physics of a truly elastic plate capable of supporting shear stresses over arbitrarily long timescales.