A new approach to the transient analysis of magnetic field is presented using the formulation of a boundary element model in two-dimensional problems. In order to solve the transient problems, state equations are formed using the boundary clement model and are solved by using the variable transformation based on eigenvalues. The computational accuracy of the proposed method is evaluated by a infinite plate model and an infinite cylinder model in which the impressed magnetic flux densities are given by a unit step function and a sinusoidal function, respectively.