The coiling process under traction is considered, with an incoming residual stress profile (that can be sufficiently compressive to make the strip buckle): a flatness defect. This paper details a 3D non-linear numerical simulation taking into account the contact of the strip on itself, with a perfect contact law. The model relies on elastic behavior at finite strain because of large rotations. Even though the behavior is elastic, the yield Von Mises criterion is computed and gives information about flatness defects (plastic zones are approximated by zones where the yield stress is exceeded). Furthermore, the paper aims at very short computation times. The modeling strategy relies (for each time step) on two analytical sub-steps. Numerical minimization procedure is used in order apply weak boundary conditions. Results are discussed with respect to a comprehensive Finite Element simulation and good agreement is observed.