Method for controlling continuum robots and systems therefrom are provided. In the system and method, a new system of equations is provided for controlling a shape of the elastic member and a tension on a tendon applying a force to an elastic member of the robot. The system of equations can be used to estimate a resulting shape of the elastic member from the tension applied to the tendon. The system of equations can also be used to estimate a necessary tension for the tendon to achieve a target shape.