Cubic structures having spherical pores ranged as BCC and FCC lattices are constructed to simulate the microstructures of cellular polymers with various relative densities. The Mooney-Rivlin strain energy potential model is adopted to characterize the hyperelasticity of the constituent solid from which the foams are made. Finite element analysis on the influences of the polymer hyperelasticity upon the macroscopic mechanical properties of the foams is carried out. Numerical results show that there is no obvious buckling plateau segment in the uniaxial compressive stress-strain curves of the regular spherical cell models as most low density foams have. Moreover, it is found that the initial tangent modulus is a power function of the foam’s relative density, and the index is smaller than 2 for lower relative density models, bigger than 2 for moderate relative density models, and closed to 2 for higher relative density models.