Continuum robots have excited increasing attention and effort from robotic community due to their high dexterity and safety. This paper designs a continuum robot equipped with an elastic backbone structure and tendon-driven system. The kinematic model of such robot is formulated and a novel approach to analyze the workspace is developed by identifying the interference between the backbone structure and the actuated tendons. An optimization function is then used to achieve appropriate compromise between the workspace and the internal space of the robot, which provides an evaluation criterion for the robot design.