The paper focuses on solving the problem of diffraction of a linear polarization electromagnetic wave on multilayer bodies of a spherical shape, i.e. a metal sphere with a dielectric cover and Luneberg lens. For this purpose tensor Green function method was used. Within the research we described the electrodynamic system verifying the expressions obtained for the calculation of electromagnetic fields. Furthermore, we compared the obtained results of calculations with the results of simulation of a similar problem in the software package ANSYS HFSS. Finally, we estimated the computational burden and computing time for solving the problem in two ways