A more accurate analysis of mechanical vibration damped by structural friction can be carried out by making use of the finite element method (FEM). A very complex model of the contact problem was developed in which non-linear characteristics of stress and strain were introduced. The model enabled determination of initial plastic deformation of rough surfaces and calculation of contact characteristics after the deformation. FEM calculations reveal considerable differences in longitudinal or angular displacements when compared to those obtained from simplified models by theoretical formulas. The energy losses determined by FEM appear to be smaller than those obtained through classical methods. It is clearly seen that the way of applying a load is decisive in estimating the energy losses for short joints. The theoretical results and those obtained by FEM are in good agreement. In both cases the difference of the hysteresis loop areas is small.