Abstract: A new method for solving the branch chain stiffness of 4-URU type flexible parallel mechanism was proposed, and the effectiveness of the method was verified by software simulation results. Firstly, the degree of freedom of the 4-URU rigid parallel mechanism was analyzed by using the screw theory, and the corresponding flexible parallel mechanism was designed by using the flexible hinge replacement method. Based on the flexible hinge stiffness matrix, the hinge stiffness matrix of the branch chain was obtained by the transformation matrix method, the stiffness of each flexible rod of the branch chain was obtained by the finite element theory, and the total stiffness matrix of the branch chain was obtained by linear superposition. Finally, the deformation of the branch chain in the X, Y and Z directions was obtained by theoretical calculation with MATLAB. The model is simulated and analyzed by ANSYS software, and the results show that the theoretical calculation is basically consistent with the simulation results. Effectiveness of the method to solve the stiffness of branch chain is verified, which provides a theoretical basis for solving the stiffness of the whole flexible parallel mechanism by using the method, and helps to study the precision of the flexible parallel positioning platform.