The paper presents a methodology to model the cutting forces by twist drills with generic point geometry. A generic definition of point geometry implies that the cutting lips and the relief surfaces can have arbitrary shapes. Such geometry is easily modeled using Non Uniform Rational B-Spline (NURBS) surface patches which give sufficient freedom to the tool designer to alter the tool geometry. The drill point has three cutting zones: primary cutting lips, secondary cutting lips, and the indentation zone at the center of chisel edge. At the indentation zone, the drill extrudes the workpiece, while at the cutting lips, shearing takes place. At primary cutting lip, the cutting is oblique while at secondary cutting lip, it is predominantly orthogonal. Starting from a computer-aided geometric design of a fluted twist drill with arbitrary point profile, the cutting forces have been modeled separately for all the three cutting zones. The mechanistic method has been employed wherever applicable to have a good correlation between the analytical and the experimental results. The force model has been calibrated and validated for conical drills. Then the model has been evaluated for a drill ground with curved relief surfaces. The theoretical and experimental results are found out to be in good conformity.