The present study deals with computer-aided design, 3D-printing, large strain numerical simulation, and experimental testing of random geometries with focus on porous materials. In particular, we attempt to assess the effect of random porous features on the mechanical response at large strain by comparing the response of well-chosen random and periodic porous geometries. We first investigate the computer-aided design process of a variety of porous geometries including random polydisperse porous materials with spherical and ellipsoidal voids, standard eroded Voronoi geometries, hexagonal honeycombs, and TPMS structures. In addition, we propose a novel computer-aided design strategy to obtain a new type of random Voronoi-type porous materials called M-Voronoi (from mechanically grown) with smooth void shapes and variable intervoid ligament sizes that can reach very low relative densities. This is achieved via a numerical, large strain, nonlinear elastic, void growth mechanical process. The proposed M-Voronoi method is general and can be applied to create both two and three-dimensional random geometries and allows the formation of isotropic or anisotropic materials. The void growth process is a consequence of mass conservation and the incompressibility of the surrounding nonlinear elastic matrix phase and the final achieved relative density may be analytically estimated in terms of the determinant of the applied deformation gradient. The extremely low densities in the M-Voronoi geometries are achieved through an intermediate remesh step in the virtual fabrication process. For this purpose, we developed a versatile and general remeshing algorithm based on the geometry reconstruction of an orphan mesh that can handle arbitrarily complex meshes, including those that contain voids or multiple phases. Moreover, the studied random geometries are general to model seamlessly a wide range of composites involving particles, multi-phase, and even polycrystals with finite interfaces under mechanical or coupled loads (e.g. magneto-electro mechanical, etc.).In the next part of the study, we fabricate the designed porous materials with a polymer 3D-printer via PolyJet technology and a UV-curable resin called TangoBlack which is a highly viscous soft polymer with brittle fracture. Meanwhile, the viscous behavior of TangoBlack is studied under uniaxial tensile, loading-unloading, and relaxation tests on a new proposed specimen geometry and is subsequently characterized by a nonlinear rubber viscoelastic model for incompressible isotropic elastomers. We then use this material to 3D-print the designed two-dimensional porous materials with square representative geometries and isotropic/anisotropic features in terms of void size and realization. The mechanical response of the fabricated porous materials is experimentally investigated by testing them under uniaxial large strain compression and low strain rates. We show that the randomness of the proposed M-Voronoi geometries and their non-uniform intervoid ligament size leads to enhanced mechanical properties at large compressive strains with no apparent peak-stress and strong hardening well before densification, while they become very close to random eroded Voronoi geometries at low densities.In the last part of this study, we investigate numerically the mechanical properties of the three-dimensional random porous geometries consisting of M-Voronoi, polydisperse porous materials with spherical voids, and classical TPMS-like geometries. The simulations are performed at large strains under compression loading while considering the matrix an elastic-perfectly plastic material without hardening. We observe enhanced plastic flow stress in the geometries with random topologies as opposed to the TPMS periodic structures. This behavior is explained by noting that deformation localizes in geometries with a periodic pattern, contrary to the random geometries which exhibit a rather diffused localization.