Surface vorticity theory, normally considered as an analysis tool, has been modified to operate as a design tool whereby the shapes of components may be found to produce a prescribed surface velocity in incompressible flow. The basis of the method is presented and checked against classical solutions for cylindrical and diamond shaped struts with fully attached flow. A procedure for turbomachine blade or aerofoil design is outlined and illustrated with back checks via Martensen’s method. The method allows specification of velocity distribution on either or both surfaces of the body. If only one surface of an aerofoil or blade is prescribed, the user is allowed to specify profile thickness also.