Taking the3-UPU/UPU parallel mechanism as an example, the structure and kinematics a-nalysis were analyzed and the Jacobian matrix of the mechanism was obtained; the parallel mechanismof local stiffness matrix and the global stiffness matrix were calculated under static equilibrium condi-tion; the local stiffness curve and global stiffness curve of 3-UPU/UPU parallel mechanism were ob-tained by the use of mathematical software MATLAB.The effect of variation of upper and lower planecircle radius on the local stiffness and global stiffness were analyzed.The results show that local stiff-ness matrix and the global stiffness depend on body posture.The variation range mechanism of localstiffness and global stiffness could be gotten for a given position;the upper and lower surface radius var-iation of body affects on the local stiffness and the global stiffness.So that high rigidity of the local andglobal stiffness can be obtained by increasing appropriately the radius of the upper and lower surfaces.