In order to develop a compact superconducting machine with high efficiency, the detailed knowledge of flux and eddy current distributions is necessary. Recently, 3-D numerical analysis of magnetic field became possible, due to, for example, the progress of fast and cheap workstations, the introduction of new element and the improvement of algorithms for solving large scale simultaneous equations. In this review, the outlines of the finite element method, features of various formulations, problems in applying the finite element method and recent developments are discussed.