The design of geometric shapes with physical constraints, such as hydrodynamic and aerodynamic constraints reflecting the functionality of the shapes, remains an important problem in CAGD. This paper presents a method to design surfaces by incorporating physical constraints involving surface normal vectors. The design of functional surfaces is formulated as a linear problem using vector calculus. The final surface is an integral non-uniform B-spline surface, which is the solution of the linear equation system resulting from the least-squares fitting of the given grid points and the normal vectors at these points. The geometric design of propeller blade surfaces in conjunction with hydrodynamic analysis illustrates the method. Copyright