The paper presents an algorithm of domain decomposition when solving the forward dynamic seismic problem in the polar coordinate system. The new algorithm is based on combination of the method of direct and of finite integral Fourier transforms. As seen from the studies conducted, if on some sites of the medium the wave propagation velocity is a constant function, the efficiency of the algorithm can be essentially increased using the domain decomposition method. Particularly, for the domains with constant velocity, the solution can be written down in the explicit form. We consider the proposed decomposition algorithm on the example of the following problem.