A method and apparatus for producing high-intensity X-rays or .gamma.-rays by accumulating a laser beam in an optical resonator having ultra-high reflectivity mirrors. With this arrangement, it is possible to produce powerful X-rays or .gamma.-rays even if the laser beam used is not powerful enough. A laser beam from a laser is injected into an optical resonator and accumulated therein. The optical resonator has an opposed pair of mirrors having a reflectivity of more than 0.999%. An electron beam may be introduced obliquely into the optical resonator and collided against the laser beam. In the interaction area thus created, X-rays or .gamma.-rays are produced due to the Compton scattering and propagated out of the optical resonator.