Purpose-Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires a very fine mesh which leads to a large system of equations, and it becomes more problematic in case of higher frequencies. The purpose of this paper is to show the numerical pertinence of equivalent models for 3D eddy current problems with a conductive thin layer of small thickness e based on the replacement of the thin layer by its mid-surface with equivalent transmission conditions that satisfy the shielding purpose, and by using an efficient discretization using the Boundary Element Method (BEM) in order to reduce the computational work. Design/methodology/approach-These models are solved numerically using the BEM and some numerical experiments are performed to assess the accuracy of our models. The results are validated by comparison with an analytical solution and a numerical solution by the commercial software Comsol. Findings-The error between the equivalent models and the analytical and numerical solutions confirms the theoretical approach. In addition to this accuracy, the time consumption is reduced by considering a discretization method that requires only a surface mesh. Originality/Value-Based on an hybrid formulation, we present briefly a formal derivation of impedance transmission conditions for 3D thin layers in eddy current problems where non-conductive materials are considered in the interior and the exterior domain of the sheet. BEM is adopted to discretize the problem as there is no need for a volume discretization.