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Lattice-type periodic metamaterials with beam-like struts have been extensively investigated in recent years thanks to the progress in additive manufacturing technologies. However, when lattice structures are subject to large deformations, computational simulation for design and optimization remains a major challenge due to complex nonlinear and inelastic effects, such as instabilities, contacts, rate-dependence, plasticity, or damage. In this contribution, we demonstrate for the first time the efficient and accurate computational simulation of beam lattices using a finite deformation 3D beam formulation with inelastic material behavior, instability analysis, and contacts. In particular, the constitutive model captures elasto-visco-plasticity with damage/softening from the Mullins effect. Thus, the formulation can be applied to the modeling of both stiffer metallic and more flexible polymeric materials. The approach is demonstrated and experimentally validated in application to additively manufactured lattice structures made from Polyamide 12 by laser sintering and from a highly viscous polymer by vat hotopolymerization. For compression tests executed until densification or with unloading and at different rates, the beam simulations are in very good agreement with experiments. These results strongly indicate that the consideration of all nonlinear and inelastic effects is crucial to accurately model the finite deformation behavior of lattice structures. It can be concluded that this can be effectively attained using inelastic beam models, which opens the perspective for simulation-based design and optimization of lattices for practical applications.