In the present study, a sensor-free force control framework for tendon-driven steerable catheters was proposed and validated. The hypothesis of this study was that the contact force between the catheter tip and the tissue could be controlled using the estimated force with a previously validated displacement-based viscoelastic tissue model. The tissue model was used in a feedback control loop. The model estimated the contact force based on a realtime estimation of catheter-tissue indentation depth performed by a data-driven inverse kinematic model. To test the hypothesis, a tendon-driven catheter (φ6 × 40mm) and a robotic catheter intervention system were prototyped and characterized. Three validation studies were performed to test the performance of the proposed system with static and dynamic inputs. The results showed that the system was capable of reaching to the desired force with a root-mean-square error of 0.03 ± 0.02N for static tests and 0.05 ± 0.04N for dynamic inputs. The main contribution of this study was providing a computationally efficient and sensor-free force control schema for tendon-driven catheters.