A strength criterion with a dependence on fabric is developed. A fabric tensor is a symmetric second rank tensor which characterizes the geometric arrangement of a porous material microstructure, or the local spatial distribution of one phase of a multiphase material relative to the other phases. The development of the strength criterion follows the method of Malmeister and of Tsai and Wu. A formula for the stress interaction coefficients introduced by Tsai and Wu is obtained. This formula relates the stress interaction coefficient to the tensile and compressive strengths in two directions, to the shear strength in the plane of the two directions, and to the fabric tensor. Heretofore there has a theoretical representation of the stress interaction coefficient in terms of other physical parameters.