Novel lightweight micro- and nanostructured materials are being used as constituents in hierarchically structured composites for providing high stiffness, high strength, and energy absorbing capability at low weight. Three dimensional SU-8 periodic microframe materials with submicrometer elements exhibit unusual large plastic deformations. Here, the plastic dissipation and mechanical response of polymeric microframe structures is investigated using micromechanical modeling of large deformations. Finite element analysis shows that multiple deformation domains initiate, stabilize, and then spread plasticity through the structure; simulated deformation mechanisms and deformation progression are found to be in excellent agreement with experimental observation. Furthermore, the geometry can be used to tailor aspects of 3D behavior such as effective lateral contraction ratios (elastic and plastic) during tensile loading as well as negative normal stress during simple shear deformation. The effects of structural geometry on mechanical response are also studied to tailor and optimize mechanical performance at a given density. These quantitative investigations enable simulation-based design of optimal lightweight material microstructures for dissipating energy.