In this two-part paper, a virtual machine tool (VMT) is presented. In part 1, the analytical foundation of a virtual machining system, envisioned as the foundation for a comprehensive simulation environment capable of predicting the outcome of cutting processes, is developed. The VMT system purposes to experience the pseudo-real machining before real cutting with a CNC machine tool, to provide the proper cutting conditions for process planners, and to compensate or control the machining process in terms of the productivity and attributes of products. The attributes can be characterized with the machined surface error, dimensional accuracy, roughness, integrity and so forth. The main components of the VMT are cutting process, application, thermal behavior and feed drive modules. In part 1, the cutting process module is presented. The proposed models were verified experimentally and gave significantly better prediction results than any other method. The thermal behavior and feed drive modules are developed in part 2 paper. The developed models are integrated as a comprehensive software environment in part 2 paper.