The complex procedures involved in the reconstructive surgery of human skin to minimize post-operative scarring are here modeled by means of an automated computational tool. A finite strain no-compression membrane model accounting for the tendency to develop wrinkling regions in the skin is presented. The constitutive behavior of the material is then described by a suitable hyperelastic incompressible potential. Transpositions of skin flaps during surgery procedures are here computationally described by a general mapping technique of the internal boundary corresponding to surgery cut. The archetypal reconstructive surgery of a Z-plasty, where a rotational transposition of the resulting triangular flaps is involved, is considered in details, along with multiple Z-plasty and rhombic flap transposition. The results are discussed in terms of optimal deformation parameters, related to stress/strain localization, displacement discontinuities and wrinkling.