Modification of the effective elastic and plastic constants of initially homogeneous and isotropic material with regularly distributed cracks is considered in the paper. The stress-strain relation for linearly elastic range is formulated as a tensor function with two independent variables: the stress tensor and damage tensor describing the current state of the cracked solid. This equation made it possible to evaluate all the elastic constants and is a starting point in the analysis of the plastic behavior of the damaged material. The appropriate yield criterion is derived in the form of an isotropic scalar function with the same variables as in the elastic range. To choose the most important terms of the general representation of this function, the energy of the elastic strain was calculated for homogenized equivalent material. This was done employing the stress-strain relation of elasticity for damaged solid proposed in the paper. The theoretical considerations were verified experimentally. To this end the material constants determined theoretically in the elastic and plastic ranges were compared with those measured experimentally for the models simulating the damaged material.