Abstract: A dynamic model of cable-driven continuum robots in hybrid position-force actuation mode is proposed. Firstly, a lumped mass matrix method is adopted in dynamic modeling of the robot. The continuously integral term of the kinetic energy for the robot is equivalently discretized into a summation form of three points, which can simplify the modeling process and improve the computational efficiency of simulations. Secondly, the mechanical relationship between the driving force and the geometrical constraint of the driving cable is analyzed, the cable actuation is equivalently modeled as linear equations of the driving parameters of motors and the tensions in cables. This actuation mode can not only accurately satisfy the constraint of the cable on the system, but also obtain the driving force of the cable without using a tension sensor, which reduces the cost and control difficulty of cable-driven robots. It is applicable to continuum robots driven by any number of cables. Finally, a comparison of the results from the numerical simulations and experiments for a cable-driven continuum robot verifies the validity of the proposed model, and the maximum error for the trajectory at the terminal point is 3.85%.