A 3-D boundary integral method (3-D BIM) capable of analyzing eddy currents in thin shields is presented. This novel approach is formulated in terms of loop currents in order to implicitly fulfill the div-free condition for quasi-magnetostatic problems. Using nonorthogonal dual grids unknowns are defined on nodes, resulting in a very efficient formulation with limited memory requirements. The proposed method is tested on an axisymmetric model showing a good agreement with the analytical solution. 3-D BIM is then applied to analyze a real case of low-frequency magnetic shielding.