The boundary element method in the framework of small strains and small displacements is used to evaluate plane frictional contract problems. Elastoplastic material behaviour is taken into account by means of an initial strain formulation and von Mises yield criterion. The amount of tangential traction at the contact surface is limited by Coulomb's law of friction. The contact conditions are defined for every pair of contact nodes. This is done in a similar way as subregions are coupled in substructuring technique. The set of equations is reduced to non-linear degrees of freedom. Due to the non-linear behaviour of friction and plasticity an incremental loading is necessary. The part of each load increment that just causes a change of contact condition is determined by an automatic load incrementation procedure. In case of elastic material behaviour incremental values are scaled linearly. The method is extended to elastoplastic material behaviour where a fast iterative scheme (Illinois algorithm) is used to determine the desired loading. Results are shown for the Hertz-like problem of two cylindric rollers in contact, a punch problem, and the contact of two teeth of an involute gear. Elastoplastic material is either defined by a bilinear stress-strain relation or by an interpolation of discrete stress-strain values by linear splines.