In order to model thin conductive non-magnetic shells, an original surface integral formulation is proposed. The method is based on a surface impedance condition which takes into account the field variation through depth due to skin effect. It is general and enables the modeling of various problems whatever their skin depth and avoiding the meshing of the air region. The formulation is compared with another integral formulation recently proposed by authors and is validated thanks to an axisymmetric finite-element method (FEM). Advantages and drawbacks of this new formulation are discussed.