This work is the first of a two part paper on cutting force prediction and feed optimization for the five-axis flank milling of jet engine impellers. In Part I, a mathematical model for predicting cutting forces is presented for five-axis machining with tapered, helical, ball-end mills with variable pitch and serrated flutes. The cutter is divided axially into a number of differential elements, each with its own feed-coordinate system due to five-axis motion. At each element, the total velocity due to translation and angular motion is split into horizontal and vertical feed components, which are used to calculate total chip thickness along the cutting edge. The cutting forces for each element are calculated by transforming friction angle, shear stress, and shear angle from an orthogonal cutting database to the oblique cutting plane. The distributed cutting load is digitally summed to obtain the total forces acting on the cutter and blade. The model can be used for general five-axis flank milling processes, and supports a variety of cutting tools. Predicted cutting forces are shown to be in reasonable agreement with those collected during a roughing operation on a prototype integrally bladed rotor.