Modification of the T-matrix method using a priori information on singularities of analytical continuation of the wave field

•A modification of the T-matrix method applicable for non-Rayleigh bodies is proposed.•Numerical comparison with standard T-matrix techniques shows the benefits of the new approach.•New approach allows performing stable universal algorithm with a high convergence rate.

A modification of the T-matrix method is proposed on the basis of the a priori information on the analytical properties of the solution. It is shown that the account for such an information allows one to obtain correct, efficient, and universal algorithms in modeling scattering characteristics for a large scale of geometries of the bodies, including essentially non-Rayleigh ones.