A novel technology for fabricating WolterⅠgrazing mirrors by an elastic ball tool was described in this paper. According to the Hertz contacting theory and Preston equation, a removal function model for tool movement on a cylinder surface was established based on the precession motion. The comparison of the theoretica1 model and the experimental results shows that the RMS distance warp between the theoretica1 removal function curve and the experimental curve is 0.101 22 μm，and its deflection ratio is 9.8%. Furthermore, the effect of different precession angles on the removal function was validated,which points out that the larger the precession angle is, the more the material are removed and the max removal point moves to the centre of contact area closely. With different precession angles, the rms deviation of max removal depth is 0.201 μm and the rms position deviation of max removal depth is 0.255 mm. The experimental results verify the feasibility of the theoretica1 model of removel function.The model can direct the fabrication of WolterⅠgrazing mirrors and can realize the deterministic material removal.