Porous materials represent a class of materials widely used in various engineering and industrial applications due to their unique properties, such as lightweight and enhanced fluid permeability, which have drawn significant attention in recent years. The effective properties of porous materials are largely influenced by porosity, the spatial distribution of pores, and the interaction between the pores and the surrounding solid matrix. Existing methods, particularly micromechanics-based analytical formulas, exhibit fundamental limitations in handling high-porosity materials and extending the analysis beyond elastic region. In this thesis, the Microstructure-Free Finite Element Method (MF-FEM) is extended to characterize porous materials by modeling two different microstructures: regular and irregular, and analyzing their properties in both elastic and inelastic regimes. The MF-FEM results are compared with analytical approaches, using available experimental results as a baseline. The comparison demonstrates that MF-FEM predictions consistently exhibit strong agreement with experimental results, whereas the accuracy of micromechanics-based formulas remains conditional and highly dependent on their underlying assumptions. Beyond its reliability, MF-FEM also provides a cost-effective numerical approach for predicting and characterizing the mechanical properties of porous materials. Moreover, this study provides a comprehensive understanding of how different pore distributions, such as regular and irregular patterns, affect the overall mechanical properties in both linear and nonlinear regimes. These insights contribute to the efficient design of porous materials for various industrial applications, including automotive, aerospace, and biomedical engineering.