We derive a boundary integral equation to compute the eigenvalues of two-dimensional billiards subjected to a magnetic field. The integral requires the Green's function of the boundary-free problem with the magnetic field pointing in the opposite direction. This Green's function is computed for the case of a constant magnetic field perpendicular to the billiard and some applications ate discussed. The elliptical billiard is then studied numerically as an example of a nontrivial application.551A6570