This paper presents the approach of building a mathematical model for a parallel robotic manipulator with flexible links and elastic joints. The links to the base are assumed to be rigid bodies, and the thin connecting rods are assumed to be flexible links. The elasticity of the transmission from the actuators to the transmission is modeled by a torsional spring and viscous damper. This is a mixed system of rigid bodies, spring, and flexible links. The deformation motion of the elastic link is approximated by shape functions similar to the finite element method. The differential equations of motion are established by combining the substructure method and the Lagrange equation of the 2nd kind for the serial multibody system. Based on the differential equation established for the parallel robot manipulator of five bars, numerical simulations were carried out to investigate the response of the system.