One situation encountered in industry is that two curves on the machined surface are known, such as the top and bottom profiles of a blade. The shape of the surface is not known and is to be determined by a tool sliding along the generating rails. In this paper, we give a detailed mathematical understanding of flank milling with flat end cutters, which we then use to develop a method for milling with such a cutter. This method slides the cutter along two rails, keeping the cutter tangent to both curves at every parameter value. Examples are given to illustrate the method, along with simulations and error analysis.