[en] The method of X-ray tomography including translucence of a controlled object by a beam of X-radiation source, detection of radiation passed through the object by means of a storage recording element under the condition of synchronous replacement of the recording element and the source or the controlled object is described. To improve quality of tomographic image translucence is carried out alternately by beams with different dimensions of the focus under the conditions of synchronization of each translucence cycle with replacement of the recorded element and the source or the object. The merit of the described radiation tomograph is that it permits to exercise by-layer radiation control with more than by an order increased resolution. In this case the X-ray tomograph makes it possible to realize highly accurate non-destructive control of thick-walled articles under the conditions of essential level of both scattered radiation background and proper or external radiation background. Besides, an electric radiographic plate in the X-ray tomograph has increased service life for the working surface of the semiconducting layer is not mechanically affected under development