The stability of an excavation cut in a rock mass comprising a regular network of joints is analyzed within the framework of a homogenization method. This method relies upon an explicit formulation of a macroscopic strength condition for the jointed rock mass considered as a homogeneous anisotropic material. Making use of two different kinds of failure mechanisms on the homogenized structure, upper bound estimates are then derived for the stability factor, which prove better than those obtained from a direct approach in which the intact rock material and the joints are considered separately.