The compressive behavior is one of most basic mechanical properties for engineering materials, and the struts of porous materials under compression may display the buckling phenomena when the porous bodies are under compressive loadings. In the present paper, a failure model of simplified structures is established for isotropic three-dimensional reticulated porous materials, and the failure modes resulting from the strut bucklings are analyzed for these materials under compressive loadings. The mathematical relationships between nominal main stresses and porosities are systemically derived for this buckling failures of these materials under uniaxial compression, biaxial compression and triaxial compression. Based on these results, the relevant loading conditions resulting in the strut buckling are further obtained for these materials under compressive loadings.