Abstract: When calculating the large volume of void regions and strongly absorbing media models by discrete ordinates method, the ray effect problems may arise, namely resulting in the flux spatial distortion such as the ripple like distribution. The nature and cause of ray effects are described and analyzed. Because the solution of the transport equation by the discrete ordinates method is conducted only along a few specific directions, and the original continuous angular variables are changed to the finite number of discrete directions, the quadrature sets are incapable of approximating the scalar flux from the discrete angular fluxes. Through research and analysis of the mainstream methods, the first collision source method is selected as major research direction. The multi-dimensional ray effect mitigation program RAY is developed, and the calculation of benchmark problem shows that RAY can mitigate the ray effects effectively.