The well-known Taylor cylinder impact test, which follows the impact of a flat-ended cylindrical rod onto a rigid stationary anvil, is conducted over a range of impact speeds for two polymers, polymethylmethacrylate (PMMA) and polycarbonate (PC). Experiments and modeling were developed to capture the deformation and fracture behavior of the cylinders after impact. The Taylor impact loading geometry imposes high levels of pressure and shear loading at impact velocities above a critical value. Introduction of shear stress at the rod-anvil interface was achieved in a new constitutive model by varying of conditions using a mediating material at the interface. This study showed a region in which there was spatial and temporal variation of both longitudinal and radial deformation that provided evidence of different failure modes.