Continuum robots have excited increasing attention and efforts from the robotic community due to their high dexterity and safety. This paper proposes a design for a type of multimodule continuum robot equipped with an elastic backbone structure and tendon-driven actuation system. The kinematic model of the robot is formulated where the maximum bending angle of a module is obtained by identifying the interference between the backbone structure and the tendons. A superposition method is then used to determine the configuration space of the robotic module. Finally, an approximation method is presented to estimate the workspace of the tendon-driven continuum robot that reduces the computational complexity in comparison with the previously used scanning method. Experiments are provided to validate the proposed methods.