Abstract: A numerical anlysis method of three-dimensional compressible viscous flow has been developed for a rectangular exhaust nozzle in which the shape of the circular-to-rectangular duct changes abruptly and its flowfield is very complex.Therefore,the sweep finite element method proposed by the second author in 1983 is employed since the governing equations are directly used to establish the element equation.In this paper,a hexahedral element of 27 nodes is adopted for spacial discretization,and applied to a C-D nozzle flowfield and several transition duct and nozzle flow fields.The results are in good agreement with the experimental data,and indicate the effectiveness and accuracy of the method.