Steady transonic flow through two-dimensional gas turbine cascades is efficiently predicted using a time-dependent formulation of the equations of motion. An integral representation of the equations has been used in which subsonic and supersonic regions of the flow field receive identical treatment. Mild shock structures are permitted to develop naturally without prior knowledge of their exact strength or position. Although the solutions yield a complete definition of the flow field, the primary aim is to produce airfoil surface pressure distributions for the design of aerodynamically efficient turbine blade contours. In order to demonstrate the accuracy of this method, computed airfoil pressure distributions have been compared to experimental results.