The primary aim of this study was to develop a unified anisotropic elasto-viscoplastic-damage model that describes the material nonlinear behavior and damage/crack growth of a reinforced polyurethane foam-based liquefied natural gas carrier insulation system. A Bodner–Partom unified elasto-viscoplastic model independent of the yield surface and loading history was expanded to an anisotropic unified model. To predict the damage growth and the crack initiation/growth of reinforced polyurethane foam, a Bodner–Chan damage model was applied to the proposed unified elasto-viscoplastic-damage model. The developed mechanical model was implicitly formulated and implemented into an ABAQUS user-defined material subroutine. To validate the proposed numerical method, the simulation results were compared with the results of a series of static uniaxial tests and dynamic cyclic tests conducted on the reinforced polyurethane foam and the liquefied natural gas carrier insulation system, respectively.