Summary: The goal of this work is to show that the numerical solution of the obstacle scattering problem based on the modified Rayleigh conjecture (MRC) method is a competitive alternative to the boundary integral equations method, and that it has numerical advantages which may be especially important in three-dimensional scattering problems with non-smooth domains, for example, with domains whose boundaries contain corners. The MRC is formulated, the algorithm based on it is described and numerical results are presented.