In this presentation, we consider elasticity problems where  frictional deformable-deformable contact (Coulomb's law) is discretised by a mortar (Lagrange multiplier) method. We present an algorithm which allies an active set strategy with a preconditioned GCR method to obtain a fast and accurate solver, Lagrangian multipliers are indeed a natural way to discretise the problem (Alart and Curnier1991), (Wriggers and Zavarise 1993) and (deSaxce and Feng 1998).