The method of solving problems of diffraction on non-Rayleight bodies, composed of several Rayleigh bodies is explained. The scattered field is constructed as a sum of fields, created by the assemblage of multifields, each of them is located in the corresponding point of one of the composite bodies. The samples involving two tangent to the generatrix of the cylinder and two touching in the single point spheres are considered. For the former of these samples, the curves of distribution current density and scatterogram are given. The curves are compared with the corresponding curves, derived using the Kirhgoff approximation.