The much debated question of whether the strength criterion of a fluid saturated porous medium, such as most geomaterials, can be expressed in terms of “effective stress,” is critically examined in this paper using the yield design homogenization theory as an investigating tool. Adopting a periodic description of the saturated porous material at the microscopic level, where the fluid phase exerts a pressure on the solid matrix making up the skeleton, a general definition of the strength properties of the porous material at the macroscopic scale is given. While some situations are identified where the “effective stress principle,” as classically formulated, remains appropriate, it is proved that for a frictional solid matrix, such a principle, even in its generalized form, is not relevant. Nevertheless, the dependence on the pore pressure can still be specified in a simple way, so that the complete knowledge of the criterion for any prescribed value of the pore pressure only requires determining the strength properties of the dry porous material. Moreover, the possibility of adopting sufficiently accurate approximations of the actual criterion by resorting to an effective stress formulation is discussed.