In this work, a multiscale model based on the Fast Fourier Transform (FFT) technique is applied to describe the mechanical behavior of porous materials. The effects of the microstructures (such as pore shape, number, size, distribution and orientation) on the overall strength of the porous medium and its microstress distribution are fully studied. The elastoplastic model is further extended by including a damage process. The influences of microstructure on the damage evolution of the porous medium are discussed and illustrated numerically. Then the proposed multiscale damage model is applied to study the macroscopic behavior of porous sandstone. According to the microstructure of the studied material, a representative elementary volume with randomly distributed spherical pores is considered. The solid phase of the sandstone is assumed to obey the Drucker-Prager criterion. Taking advantage of the FFT-based method, the evolution of generated damage is clearly illustrated during the loading process at the microscopic level. Comparisons between numerical results and experimental data show the efficiency of the proposed numerical model.