The inventive device comprises an X-ray tube (1) provided with a planar fire anode (2). A first collimator (5) having perforated channels (4) is disposed between said X-ray tube and a studied object (8). A unit (16) provided with a detector array (17) detects secondary radiation which is excited in the object (8). A second collimator provided with perforated or slotted channels (23) is arranged between said object and the unit (16). The location of the radiation spot (3) of the X-ray tube (1) on the surface of the anode (2) is scanned with the aid of a electron beam control unit (6). A signal carrying information on the density of substance of the object (8) appears in the cross-section between the continuation of the channel of the first collimator on whose input the radiation of the tube (1) is present and the continuation of one of channels of a second collimator (9). Said signal reaches the input (18) of a data processing block (19.1) which is embodied in the form of part of a data processing and display unit (19). Information on the current position of electron beam is transmitted from a unit (6) to the input (20) of the block (1.91). In another variant, such data is contained in the beam modulation of the tube (1), the connection between the unit (6) and the block (1.91) being absent. The distribution of the density of the substance through the volume of the object (8) is determined in the block (1.91). The result is displaced on a monitor (19.2). The inventive device can also comprise an additional collimator (9a) and a means (16a) provided with a detector (17a), a means (28) for detecting the radiation of the tube (1) which passes through the object (8) and for producing the projection (29) of the internal structure thereof.