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Materials capable of dramatically changing their stiffness along specific directions in response to an external stimulus can enable the design of novel robots that can quickly switch between soft/highly–deformable and rigid/load–bearing states. While the jamming transition in discrete media has recently been demonstrated to be a powerful mechanism to achieve such variable stiffness, the lack of numerical tools capable of predicting the mechanical response of jammed media subjected to arbitrary loading conditions has limited the advancement of jamming-based robots. To overcome this limitation, we introduce a 3D finite–element-based numerical tool that predicts the mechanical response of pressurized, infinitely–extending discrete media subjected to arbitrary loading conditions. We demonstrate the capabilities of our numerical tool by investigating the response of periodic laminar and fibrous media subjected to various types of loadings. We expect this work to foster further numerical studies on jamming–based soft robots and structures by facilitating their design, as well as providing a foundation for combining various types of jamming media to create a new generation of tunable composites.