Abstract: The basic equations in the integral form governing the three-dimensional flow and the flow on the thin streamfilament with S1 or S2 surface as its central plane in a turbomachlne are presented. From these equations the relations between the parameters of fluid ahead and behind a shock are derived for each cases. It is seen in thses relations that the shocks on the stream surfaces are not the same as those in the two-dimensional oblique shocks and the correlations between the adjacent streamfilaments and between the two kinds of the stream surfaces are closer In order to solve the three-dimensional flow with shocks exactly it is necessary to calculate respectively along each kind of stream surfaces the two-dimensional flows in accordance with the three-dimensional flow and to iterate these computations. It is pointed that calculating the flow along the stream surface with a given shape is not correct. In addition, the assumption of the surface of revolution can not be hold. Finally, considering the advantage of the surface of revolution in computations, the concept about the generalized surface of revolution is introduced.