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In order to compute electromagnetic problems in presence of thin conductive and magnetic shells, a new integral formulation is proposed. Based on the principle of shell element, the formulation is general and enables the modeling of various problems for any skin-depth, avoiding the air region meshing. The formulation is validated thanks to an axisymmetric FEM and compared with another shell formulation implemented in a 3D FEM. Advantages and drawbacks of this new formulation are discussed.