The streaming rays(SR) method is improved and extended to multigroup, anisotropic scattering, and three-dimensional angular space(x-y-z(infinite))problems. This method is applied to the shielding problems in which the ray effect occurs seriously. For verification, the results of MORSE-CG code are used as reference solution and the results of TWODANT code are compared. The results show that solutions of the SR method are much better than those of the TWODANT code and are in good agreement with those of the MORSE-CG code. Also, to reduce computing time, two acceleration algorithms are implemented in the SR method : the standard coarse-mesh rebalance and a new angular two-grid acceleration.