In the present paper a method is presented for the analysis of rock joints and interfaces. The mechanical response of rock joints and interfaces involves phenomena of nonclassic nature as debonding and slip along the interfaces, which can be completely described by nonmonotone possibly multivalued (e.g. sawtooth) phenomenological constitutive laws, the so-called complete laws, which result from the respective experimental stress-stain diagrams. Due to the lack of monotonicity of these laws, the rock interface problem cannot be studied by means of the classical variational methods and therefore, the need for a generalization of the classical variational theories to cover also such constitutive laws arises. This can be achieved by means of the notion of generalized gradient which was already applied to the solution of a large number of structural analysis problems involving nonconvex and nondi~erentiable energy functions. First the interface behaviour is modelled through nonconvex su~~otentials describing the debonding and/or stick/slip phenomena. 'T%en the hemivariational inequalities are formulated and some methods for the numerical treatment are proposed.