Multi-body-system (MBS) simulation is widely used in the railway industry. One of its major topics is the assessment of rolling contact fatigue (RCF). This damaging process is linked to plasticity. MBS wheel–rail contact models usually neglect plasticity as it does not change the vehicle behaviour. With the proposed method, contact stresses are consistent with a perfect plastic law. This new method has been recently detailed: it is an extension of the STRIPES semi-Hertzian (SH) model. A multi-Hertzian (MH) variant is here described, which is less exact but faster than the SH method. This new method has been implemented in a MBS package without resulting in a much longer execution time than elastic models.