Additively manufactured auxetic structures exhibit exceptional mechanical properties, such as lightweight design, enhanced energy absorption, high shear stiffness, and excellent indentation resistance. Unlike conventional materials, auxetic structures feature a negative Poisson’s ratio, enabling unique deformation characteristics through tailored geometries. This study investigates the mechanical behavior of two lattice designs: re-entrant auxetic and conventional hexagonal honeycomb structures. Finite element analyses in both 2D plane strain and 3D were performed using multi-field displacement-pressure elements. The structures were modeled using hyperelastic and rate-independent plasticity constitutive laws calibrated with experimental uniaxial tensile test data. The simulations involved loading in both longitudinal and transverse directions, incorporating self-contact between the struts and contact with the loading plates by the contact domain method. The results demonstrated a strong agreement with the experimental findings. The re-entrant auxetic structure exhibited a negative Poisson’s ratio and superior energy absorption efficiency compared to the hexagonal honeycomb. These insights contribute to a reliable theoretical framework for designing high-performance lattice materials with direction-dependent mechanical properties.