Abstract: This paper presents an approach that transonic relaxation methodis applied to compution of the flow field around cascades on steady andunsteady flows.On steady flow small disturbance hypothesis in normality ofchord is assumed and on unsteady flow small disturbance hypothesis of line-arized unsteady component is assumed,so that the numerical solution proce-dure is simplified.Because the relaxation method saves computer time andmemory space,it is benefit of wide application in engineeing.

Key words: Subject Term Relaxation method, Transonic flow, Cascade flow, Computational mathematics, Application.