An incremental, nonlinear finite element procedure is developed, suitable for deformation, stress and stability analysis of embankment dams with waterproof elements other than earth. The procedure is applied for analysis of hypothetical rock-fill dams with asphaltic facing and an internal asphaltic core vertical and inclined. Studies are carried out to understand the prototype behaviour of these types of rock-fill dams. Both rock-fill and asphalt behaviour is modelled by using hyperbolic relations. Due to interelement compatibility, the conventional use of finite element method (FEM) makes impossible the consideration of the effect of differential displacements along the interface of different materials. In order to get a correct and complete analysis in the interfaces rock-fill rigid foundation, asphaltic facing concrete cut-off and asphaltic core transition granular material, joint elements are introduced. In the described studies, a parabolic isoparametric joint element without thickness, numerically integrated, is used. The used model of FEM enables us to get a clear picture of the behaviour of the dam body and the waterproof elements during the incremental construction procedure, as well under the exertion of the water forces. The joint elements enable us to consider the differential displacements along the interface of different materials and contribute to decreasing the number of iterations.