Abstract: A static model and a mathematical model of static deformations of plane joints are presented in this paper based on the fundamental theory of mechanical joints. The static stiffness matrix of plane joint is also determined, which provides a theoretical basis for the selection of optimal design scheme, the prediction of design effects and the seeking of sound design parameters in CAD of machine tools. The software developed by the authors can be employed as a basic program block for the analysis and forecast of the general characteristics of a machine.