The elastostatic stiffness modeling of a 2UPR-RPU parallel manipulator with 2R1T three degrees of freedom was studied based on the screw theory and strain energy, considering the compliance of the bars and joints. Firstly, the limb constraint wrenches was formulated based on the screw theory. Secondly, the strain energy of bar was formulated by material mechanics, and joint by mapping the constraint wrenches to the joint space, and concentrated limb stiffness matrix corresponding to the constraint wrenches was thus obtained by summarizing the strain energy of bars and joints in the limb, and combining with the Castigliano second theorem. Finally, the overall stiffness matrix was assembled based on the virtual work principle. The theoretical result was verified by commercial ANSYS software. The strain energy factor index was defined as the strain energy of the elastic component account for total strain energy for illustrating the influence of each elastic component on the stiffness performance of the mechanism. A fourdimensional image of slice distribution was presented, the influence of each elastic element on the stiffness performance of the 2UPR-RPU parallel mechanism was quantitatively evaluated from the perspective of strain energy. Finally, the global strain energy factor indices of the mechanism under different external wrenches were presented to find the elastic component with the maximum compliance. The proposed modeling provided a new ideas for improving the stiffness performance of the mechanism more effectively.