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This paper describes a boundary element method using vector variables for three-dimensional analysis of eddy current distributions. In the boundary element method, electric field vectors and magnetic flux density vectors are used as unknown vector variables on the boundaries of two materials. The formulation is performed by using the vector Green's theorem. After determining electric field vectors and magnetic flux density vectors on the boundaries, eddy current distributions in the conductor are computed. The computation results of a conducting sphere model agreed exactly with analytical solutions. As an example of three dimensional eddy current problems, the analysis of a conducting cube model was done.