The objective of this work is to numerically investigate the elastoplastic behavior of closed-cell foams. Anisotropic geometry with ellipsoidal pores is considered and the contribution of the inner gas pressure within the cells is incorporated to the model. Based on face centered cubic (FCC) arrangements of pores and the finite element method, macroscopic elastic constants and initial yield stress against the relative density and cell aspect ratio are discussed in this paper. Through a systematic study we find that the initial yield stress is dependent on the loading direction. The inner gas pressure results in the asymmetry of uniaxial tensile-compressive stress-strain curves and significantly affects the initial yield stress of the foams for different loading directions.