The method enabling one to obtain tomographic images of an electrically conductive or dielectric object by the excitation of the variable magnetic field inside it and by measuring the resulting field around the object is described. The main equations and theoretical estimations are given. It is shown that phasesensitive measurements should be used in magnetic induction tomography. The measuring system providing the data set necessary for the image reconstruction is discussed. Under the conditions of the measurements discussed in this paper, image reconstruction is possible with the use of a simple method of convolution and back-projection along magnetic lines. Computer simulation demonstrates the visualization of the conductivity distribution by the method of magnetic induction tomography with phase measurements.