The geometrical error modeling of the numerically controlled (NC) lathe is the key technique to kinematics design, precision analysis and error compensation. The study gives out the modeling process of the generally geometrical error model based on the multi-body system theory for the multi-axis NC machine tools. By the multi-system theory, using the low series body arrays to describe the complex mechanical system, the article has finished the geometrical error modeling of the numerically controlled lathe, analyzed the influence on the model of error of perpendicularity between the linear axes. The modeling method is highly-efficient and can not be affected by the structure of the NC machine tools. The error compensation and command correction can be implemented by the geometric errors model.