The compressive behavior is one of the most basic mechanical properties of engineering materials. With the simplified structural model, the compressive failure mode is analyzed for isotropic three-dimensional reticulated porous materials, and the mathematical relationships between nominal main stress and porosity are obtained for these materials at shearing failure under uniaxial compression, biaxial compression and triaxial compression, respectively. The results show that, the porous body of brittle material species shows the tensile fracture mode of pore struts, and the porous body of ductile material species may display the shearing fracture mode of pore struts. The correspondingly obtained criteria of strength design can be referred to in applications of these materials under respective loading failure modes.