Abstract: Stiffness is one of the important characteristics of the parallel mechanism. Taking the 3-TPT parallel mechanism as the research object, the static stiffness is solved by the stiffness matrix method. The static analysis is carried out using the principle of virtual work, and the statics Jacobian matrix is solved to deal with the connection between the power and the load of the parallel mechanism when the force is balanced. At the same time, the stiffness matrix method is used to construct the static stiffness model of the mechanism, and the stiffness of the branch chain and the whole of the mechanism is solved. Through research, it is found that the active part has the greatest influence on the stiffness of the branch chain; and when the external force on the end is determined, the force deformation of its end decreases with the increase of the x, y, z coordinates of the force point. This pair of parallel mechanisms provides a theoretical basis for design in production practice.