An algorithm that models three-dimensional contact with friction, including cases where large deformations occur is proposed. The algorithm is an extension to three-dimensions of an algorithm for contact previously proposed by Ponthot and Hogge [1]. The present algorithm can be used in implicit or explicit codes, when contact between a rigid and a deformable body or among deformable bodies (multibody contact) is to be determined. The penalty method is used as the contact±friction formulation. Constitutive relations for contact±friction and integration of these relations in a corotational reference system are detailed. In order to provide a good convergence rate, the contact±friction stiness matrices used are consistent with the time integration process. A simple and fully explicit form was obtained for these matrices. For contact problems involving rigid and deformable bodies, interpenetrations are detected using an iterative procedure. For frictionless multibody contact, a new element that simpli®es the gap calculation, eliminating iterative procedures, is proposed. Comparison with benchmark results and the solution of practical examples demonstrate the eectiveness of the algorithm.