In the design of turbomachinery blades, it is highly desirable that the second derivative of the profile shape is continuous. To meet this requirement, the present method uses Bernstein polynomials to describe the surface of the blades. Pressure and suction sides are formed of one segment each to ensure a continuous surface. The analytical description of the blade offers many advantages in a computer-aided design process, because any geometrical operation — intersection with other bodies, rotation, displacement and projection — is relatively simple. The design program is written in the EUKLID programming language which was developed for elegant and simple treatment of geometrical problems. For example, the language includes standard routines for vector operation, intersection of bodies and various graphical displays. Punched tape for NC machines can be generated. With an example, the design process for a turbine blade is explained and the different capabilities of program are demonstrated.