In this paper, the phenomenon of cumulative slip of solids under cyclic load is considered. The topic concerns with the relative displacements of two solids maintained in contact by friction. The statement of Melan's theorem is first given under the assumption of full contact under Tresca friction. It suggests again the definition of a safety coefficient with respect to shakedown. The safety coefficient can be computed by static or kinematic approaches. For Coulomb friction, these general results do not hold. Numerical calculations by step by step integration show that the asymptotic behaviour with or without shakedown could be obtained very quickly, after some cycles.