In connection with the calculation of x-ray transition radiation (TR) generated in a complicated configuration radiator, a new method for the calculation of the transition electromagnetic field, is suggested which is analogous to the eikonal approximation in quantum mechanics. The method is based on the fact that, in the x-ray TR frequency region h..omega.. > or approx. = 0.7 keV, the dielectric constant of the usual substances differs very slightly from unity: vertical-barepsilon (..omega..) - 1vertical-bar very-much-less-than 1. The use of this condition allows one not only to obtain the well-known results of the x-ray TR theory in a simple way, but also to solve those problems for which the existing exact methods are either very complicated or they are invalid. The eikonal approximation is applicable for the calculation of the work performed by a charged relativistic particle passing through a plate or an arbitrary medium.