A comprehensive three‐dimensional formulation for the strength criterion of regular jointed rocks is derived in this paper. The approach is based upon the implementation of the homogenization method of periodic media within the framework of the yield design theory. A rigorous explicit expression of the macroscopic criterion is given as a function of the strength properties of the intact rock and of the joints modelled as interfaces. Attention is focused on the particular case of an infinitely resistance intact rock. It is shown in particular how the relevant velocity jumps for the homogenized medium can be characterized from the introduction of the set of admissible stress vectors acting upon an elementary surface. The results make it possible to perform the static and kinematic approaches in order to address the stability analysis of rock masses cut by sets of regular joints, even for the three‐dimensional geometries.