The continuum models that take plastic material behavior into consideration are derived to analyze periodic octet-truss lattice materials under multiaxial loading. The main focus of this study is to investigate the basic topology of unit cell structures having the cubic symmetry and to formulate the analytical models for predicting pressure load-dependent stress surfaces accurately. The discrete lattice materials are converted into equivalent model continua that are obtained by physically homogenizing the property of the unit cell structures. The effective continuum models contain information on the mechanical characteristics of internal truss members with respect to axial stiffness, internal stress variable, structural packing, and material density at the microscale level. With the hardening material model introduced in the homogenization process, the plastic flow acting on the microscopic truss members gives rise to extend the elastic domain of the analytical stress function derived from homogenize constitutive equations at the macroscale level. Analytical stress predictions show excellent agreements with the results obtained from finite element (FE) analyses.