A new axisymmetric throughflow method for analyzing and designing turbomachines is proposed. This method utilizes body-force terms to represent blade forces and viscous losses. The resulting equations of motion, which include these body-force terms, are casted in terms of conservative variables and are solved using a finite-volume time-stepping scheme. In the inverse mode, the swirl schedule in the bladed regions (i.e. the radius times the tangential velocity rVθ) is the primary specified flow quantity, and the corresponding blade shape is sought after. In the analysis mode, the blade geometry is specified and the flow solution is computed. The advantages of this throughflow method compared to the current family of streamline curvature and matrix methods are that the same code can be used for subsonic/transonic/supersonic throughflow velocities, and the proposed method has a shock capturing capability. This method is demonstrated for designing a supersonic throughflow fan stage and a transonic throughflow turbine stage.