Recovery of an internal structure of three-dimensional object with operators of the mixed approximation of functions by Bernstein polynomials from 3 variables is researched on the basis of the two-dimensional tomograms made in a system of three cross-perpendicular squares. Use of this recovery method increase an exactitude of the image and will enable to rebuild structure of 3D-object in planes which do not belong to the indicated system of squares. Such problem originates, for example, at maintenance of medical tomographs when the information is necessary for an improvement of the diagnosis about an internal structure of a skew field in planes which were not investigated earlier for the doctor.