This article deals with residual stress evaluation within the framework of numerical simulation of the coiling process of steel. Plastic deformations along with multiphase transitions are responsible for large irreversible strain leading to major residual stress issues. A nonlinear mixed analytical/numerical approach is developed to compute residual stresses generated by different contributions of inelastic strain occurring during the coiling process (including both winding and cooling). In particular, transformation-induced plasticity is taken into account. Contact stresses at the interfaces between layers are updated at each time step by a minimization procedure. The analytical part of the proposed strategy is validated by comparison with a finite element computation. Then a coil composed of 196 layers is considered under typical industrial conditions. Numerical results are discussed to present the industrial application of the proposed approach.