AbstractA numerical method is presented for the design of thin turbomachinery blades with specified whirl velocities across the blade span. The numerical scheme involves iteration between the directs solution of a finite‐volume method developed earlier on by Soulis1and a design solution.The finite‐volume method, which is a combination of finite elements and finite differences, solves the three‐dimensional, inviscid, steady arid potential flow through turbomachinery blade rows in the incompressible, compressible and transonic flow range. In the design step, the whirl velocity distribution is specified across the blade span (Dirichlet boundary condition). The design procedure yields a new set of co‐ordinates for the blade geometry which are used in the next iteration of the direct solution. However, in the present analysis only thin turbomachinery blades are designed, although a fully three‐dimensional numerical method is used (the whirl velocity components of the flow field are averaged over the blade suction and pressure surface).The numerical method has been used to design free‐vortex thin turbomachinery blades. Results show that the new numerical procedure is a comparatively economic and reliable method for designing thin turbomachinery blades. It may form the baseline for complete three‐dimensional turbomachinery