Various design modifications have been proposed for tendon-driven continuum robots to improve their stiffness and workspace. One of them is using locking mechanisms to constrain the lengths of rods or passive backbones along the robot. However, physics-based models used to predict these robots' behaviour commonly assume that the curvature of the locked portion does not change during robot actuation or that the effects of friction and gravity are negligible. In addition, these models do not consider the variations in twist on force application. In this letter, we propose a 3D static model for tendon-driven continuum robots experiencing locking due to length constraints on rods along their backbone. The proposed model is evaluated on prototypes of length 240 mm, with up to three locking mechanisms and has an accuracy of 3.63% w.r.t. length. Using the proposed model, a compliance analysis is performed studying the evolution of the robot compliance with the position of the locking mechanisms. An actuation strategy is proposed that can allow the robot to achieve the same shape with different compliance.