The present study deals with the following aspects. The non-linear finite elements method, using initial stress approach, is introduced in detail. The elasto-plastic matrix with non-associated flow rule is extended to the case in which the surface of failure criterion involves singular points. The general theory is applied to establish the elasto-plastic matrices of the jointed rocks, viz. laminar and non-tension mediums, being semi-positive definite. Two simple examples show that the processes used in references  and  may lead to negative strain energy in some of the elements. By reducing the thickness of a rectangular element to zero, the matrix [B] for joint elements in  is recovered, and the stress-strain relations for them are also given, thus we have derived stiffness matrix of joint elements. Finally, the brief comments are given for some programs written on the basis of the present mechanical model together with some examples worked out by the authors in applying the method to the stability analysis of the rock foundations, slopes and underground structures.