A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE) theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE) theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes