The paper deals with the development of a physical method for tomographic imaging the dielectric objects in the microwave region, specifically, in upper X and lower Ku ranges. To test the proposed method an experimental setup has been made. The principal elements of the setup are 6 receive antennas and 2 masses of transmitters including 256 transmitting elements which operate at 32 frequencies of the microwave range between 8 and 18 GHz. Tested dielectric samples were made of wax and polyvinylchloride with known dimensions and permittivity values. The performed experiments demonstrated both the possibility of tomographic imaging and of permittivity determination in principle, and some disadvantages related to imperfections in the experimental setup. To improve the experimental setup we plan to rig some additional receive antennas and to optimize the arrangement of the principal elements. dielectric object, TOMOGRAPHIC IMAGE, microwave region, receive antenna, permittivity.