We have done an analysis of the results on the motion of a charged particle in an external field of plane and arbitrarily polarized electromagnetic waves of high intensity in the presence of an external uniform static magnetic field. A point of interest was a solution of the equation of the motion of a charged particle in the field of the electromagnetic wave and a uniform constant magnetic field. We investigated the interaction of high intensity laser pulses with solid targets in relation to the practical development of multi-frequency lasers and the technology development of laser modulation. The problem in question is topical because of the wide practical application of high-temperature plasma forming on the surface of the target, and the search for new modes of laser-plasma interaction. The formulae for the average kinetic energy of a relativistic particle, depending on the initial data, for the amplitude of the electromagnetic wave and for the wave intensity and its polarization parameter were obtained. The dependence of the average kinetic energy on the intensity of the electromagnetic wave in the uniform constant magnetic field was derived.