This paper presents a refined model of the stress distribution in cylindrical assemblies. Compared to the first model developed by the authors, the present study takes into account the radial stress in the assembly, sigma((i))(rr)(r). We first write all the components of the stress field function of the axial stress, sigma((1))(zz)(z), in the first tube, and then we introduce these components into the potential energy formulation. We apply a variational method to the potential energy of deformation and solve the differential equation to obtain the minimum and at the same time the axial stress, sigma((1))(zz)(z). This model predicts better the intensity and stress distributions in the assembly. (c) Koninklijke Brill NV, Leiden, 2009