A formulation for multibody contact systems including friction, and associated numerical methods is given. Candidate contact zones being defined, the algorithm determines the real contact parts together with the normal and tangential contact forces. The non-penetration conditions are set as unilateral conditions and lead to a complementarity problem known as the Signorini problem, whereas friction is described by Coulomb inequalities. The weak formulation is an implicit variational inequality including an undifferentiable term. The numerical approximation is based on an incremental formulation associated to a fixed point problem on the sliding limit. In this context, the main problem to be solved is the minimization under constraints of a quadratic functional including an undifferentiable term. Projection techniques associated to successive overrelaxation are used and a few accelerating procedures are described. The behaviour of a bolted junction in pressure vessels is analysed. It is a four-part structure connected by three contact areas. The different friction coefficients are identified during the first loading step through comparison with experimental data. The validation of the Coulomb model is then confirmed during the following loading steps.