Two-dimensional (2D) regular and random cell models composed of circular cells are developed to simulate the microstructure of polymer foams. Two-parameter Mooney-Rivlin strain energy potential model is employed to characterize the hyperelasticity of the solid of which the foams are made. Finite element method is used to simulate the large deformation of the foams. Numerical results show that the strain rate sensitivity of the polymer foam is weak as rate independent constitutive model is introduced to describe the mechanical performance of cell material. ‘X’-, ‘I’-, and ‘V’-shaped bands are observed in regular foam models at a low, high and moderate impact velocities, respectively; whereas ‘I”-shaped modes appear in random cell models at a high impact velocity only.