In several electromagnetic applications, field quantities are confined in layers that are thin with respect to other geometrical dimensions. The numerical solution of these phenomena has led to the development of special formulations. Among these, the surface impedance boundary conditions (SIBCs) have been extensively investigated in the past decades, often coupling them to other techniques for the analysis of volumes, such as the finite-element or boundary element methods. In this paper, the SIBCs are presented by the light of finite formulation and extended to include the considered magnetic nonlinearity