Theoretical and experimental research on the motion and radiation of charged particles in a crystal attracts at present growing scientific attention .1 The existence of a high-frequency radiation from a crystal predicted by M. A. Kumakhov4 has been confirmed by a recent Soviet-American experiment .2,3 However, even though qualitative agreement with the theoretical predictions has been proved, a complementary analysis of the motion and radiation of relativistic particles seems to be necessary. In Ref. 5 the equations of motion are found assuming that a particle does possess relativistic longitudinal and nonrelativistic transversal energies. In Refs. 6, 7 the radiation intensity is studied by quantum mechanics methods.