Dynamic models of the cable-driven continuum robots are commonly employed for those robots that are actuated by the cables’ forces. In this paper, a dynamic model is proposed for the cable-driven continuum robots actuated by position and/or force actuated cables, which is appropriate for any desired number of actuation cables and their routing. The robot is supposed to have an extensible backbone with the capability of bending and torsion in three-dimensional spaces. The proposed dynamic model is developed based on the Euler–Lagrange formulation of equations of motion taking into account all the effective forces including gravity force, cable actuation forces, external forces, and cable-disk friction forces. Furthermore, an iterative numerical solution method is presented for the dynamic model which requires much less memory and computational effort in comparison with the closed-form methods. The static model of the robots is also developed based on the dynamic model and the results obtained from the simulations and experiments are used for the validation of the static and dynamic models. The final results indicate the accuracy of the proposed models for estimating the kinematics, statics, and dynamics of the cable-driven continuum robots.