This paper presents a new methodology for analytically simulating multi-axis machining of complex sculptured surfaces. A generalized approach is developed for representing an arbitrary cutting edge design, and the local surface topology of a complex sculptured surface. A NURBS curve is used to represent the cutting edge profile. This approach offers the advantages of representing any arbitrary cutting edge design in a generic way, as well as providing standardized techniques for manipulating the location and orientation of the cutting edge. The local surface topology of the part is defined as those surfaces generated by previous tool paths in the vicinity of the current tool position. The local surface topology of the part is represented without using a computationally expensive CAD system. A systematic prediction technique is then developed to determine the instantaneous tool/part interaction during machining. The methodology employed here determines cutting edge in-cut segments by determining the intersection between the NURBS curve representation of the cutting edge and the defined local surface topology. These in-cut segments are then utilized for predicting instantaneous chip load, static and dynamic cutting forces, and tool deflection. Part 1 of this paper details the modeling methodology and demonstrates the capabilities of the simulation for machining a complex surface. Part 2 details both the model calibration procedure and discusses a case study of process optimization through feed rate scheduling.