Because of their many unique and desirable properties, engineering polymers have increasingly been applied in applications where impact behavior is of primary concern. In this paper, the impact behavior of a glassy polymer acrylonitrile-butadiene-styrene (ABS) and a semicrystalline polymer alloy of polycarbonate and polybutylene-terephthalates (PBT) are obtained as a function of impact velocity and temperature from the standard ASTM D3763 multiaxial impact test. As computer simulation of destructive impact events requires two material models, a constitutive model and a failure model, uniaxial mechanical tests of the two polymers are carried out to obtain true stress vs. true strain curves at various temperatures and strain rates. The generalized DSGZ constitutive model, previously developed by the authors to uniformly describe the entire range of deformation behavior of glassy and semicrystalline polymers for any monotonic loading modes, is calibrated and applied. The thermomechanical coupling phenomenon of polymers during high strain rate plastic deformation is considered and modeled. A failure criterion based on maximum plastic strain is proposed. Finally, the generalized DSGZ model, the thermomechanical coupling model, and the failure criterion are integrated into the commercial finite element analysis package ABAQUS/Explicit through a user material subroutine to simulate the multiaxial impact behavior of the two polymers ABS and PBT. Impact load vs. striker displacement curves and impact energy vs. striker displacement curves from computer simulation are compared with multiaxial impact test data and were found to be in good agreement.