Continuum robots mimic the principle of a special biological structure known as the muscular hydrostat. These robots have an ability to bend at any location on along its backbone and have potential applications in disaster relief, medical surgeries and nuclear waste disposal. This thesis presents the modeling and verification of a multi-section continuum robot by applying the Cosserat theory of rods. Next, 2D verification is performed on a continuum robot based on a backbone composed of a nickel titanium alloy. In addition, the thesis develops the theoretical foundations for a cable-driven continuum robot by studying the effects of cable guide mass which cause additional deformation of the robot The results of this thesis show that the multi-section model is accurate within 3.4% in predicting the Cartesian tip coordinates, and the model with the cable guides accurate within 1.26% error in predicted versus the observed Cartesian tip coordinates of the backbone.