Based on Huygenes¡¦ principle, the authors present an accurate and computationally efficient method to compute the shortest raypath and traveltime in a two- and three-dimensional (2-D and 3-D) space of a discrete block model. The efficiency of the method is achieved through approximation, while the accuracy of the calculated traveltime soley depends on machine precession. the accuracy of the raypath is realized by the small increment in the orientation of the ray incidence. Whether the computational efficiency and accuracy can be justified depends on the model¡¦s complexity and requirements in its own application. In addition, the feasibility of implementing the algorithm on the Cray T3D Massively parallel Processors (MPP) is proposed.