This paper deals with theoretical foundations of micromechanical constitutive modeling of porous polycrystalline ceramic materials under compression. The porosity of the material is assumed to be closed and distributed in grains and along grain boundaries. It strongly influences both material elastic features and microcrack growth. The deformation process includes elastic phase, dislocation band creation, and microcrack initiation, the crack-development phase leading to crack kinking and finally to failure. As an example, the quasi-static loading process of MgO ceramics is analyzed.