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Porous non-woven fibrous media are widely used in various industrial applications such as filtration, insulation, and medical textiles due to their unique structural and functional properties. However, predicting the mechanical behavior of these materials is challenging due to their complex microstructure and anisotropic nature. In this study, a computational model is developed to simulate the mechanical response of porous non-woven fibrous media under external loading. The model is based on the finite element method and takes into account the geometric and material properties of the fibers and the void spaces between them. The effects of various factors such as fiber size, porosity, and fibers’ intersection ratio on the mechanical behavior of the material are investigated. The results reveal that the material’s porosity and fibers’ intersection ratio are the most significant factors influencing its mechanical properties. Additionally, the increase in fiber diameter has a relatively minor effect on the material’s elastic properties. However, such changes in elastic properties are primarily attributed to the increase in randomness within the fibrous network, which is directly related to the fiber diameter for the investigated structure. The proposed computational model predicts the mechanical properties of porous non-woven fibrous media and can provide invaluable insights into the design and optimization of porous non-woven fibrous media for various scientific and engineering applications.