Many engineering materials contain families of pores at different scales. In this study, a numerical homogenization analysis method is developed to describe the effective elastic and plastic properties of a class of porous materials with two populations of pores at two separated scales. The solid phase at the micro-scale is described by the Drucker-Prager criterion. An analytical plastic criterion is used for the effective plastic criterion of the porous matrix with the micro-porosity. The influence of the meso-porosity, which is embedded in the homogenized porous matrix, is investigated by developing a numerical method based on the Fast Fourier Transform (F F T). With this two-step homogenization method in hand, a series of numerical assessments are performed. The relative roles of both families of pores on the macroscopic elastic properties and plastic yield stresses for a given total porosity are particularly investigated and compared with existing analytical solutions. Moreover, the proposed numerical method is extended to describe the local strain fields of microstructure with compressible porous matrix under various loading paths.