The kinematic errors of the linear axis play a key role in machining precision of high-end CNC (Computer Numerical Control) machine tool. The quantification of error relationship is still an urgent problem to be solved in the assembly process of the linear axis, especially considering the effect of the elastic deformation of rollers. A systematic error equivalence model of slider is proposed to improve the prediction accuracy for kinematic errors of the linear axis which contains the base, the linear guide rail and carriage. Firstly, the geometric errors of assembly surface of linear guide rail are represented by small displacement torsor.According to the theory of different motion of robots, the error equivalence model of a single slider is established, namely the geometric error of assembly surface of linear guide rail and the pose error of slider is equivalent to the elastic deformation of roller. Based on the principle