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Residual stresses are a crucial matter regarding rolling contact fatigue, either for ratchetting and low cycle fatigue failures as well as for high cycle fatigue. In this paper, an algorithm to compute the residual stresses under two dimensional rolling and sliding contact is proposed, based in some modifications over a previous semi-analytical approach forwarded by Jiang and Sehitoglu [1],[2]. The modified model here proposed, which takes into account a full nonlinear kinematical hardening, is stable and gives accurate solutions for high values of plastic loads. The method was also validate with finite element data extracted from the literature, showing a very good agreement.