Minimization of tool path errors in high speed machining necessitates optimal design of machine tools and application of advanced control strategies. Analytical models that accurately represent interactions between the machine tool, workpiece and cutter prove necessary to accomplish these tasks. Two distinctive methods of modeling, suitable for the design of mechanical hardware and advanced control systems, are presented. One of these methods is highly intuitive and allows interactive model building . The other method is more accurate and comprehensive but does not provide easy insight into the model development process and requires advanced software for performing symbolic computations . Together, these methods form the basis of a systematic and stepwise modeling methodology and environment, and provide information needed for optimal design of a wide range of machine tools. Application of both methods to the minimization of tool path errors and control system design is illustrated with examples.