Angular displacement sensing and contact force sensing in robotic surgery is important for finding the conformation of the tool and for closed loop control. Current techniques for measuring large deflections, such as electromagnetic tracking, involve bulky external reference equipment. This paper discusses the design, dynamic modeling, and kinematic simulation of a compact two-axis bend sensor constructed from layers of carbon black filled polyurethane for determining the bending angle of a cable-driven continuum robotic endoscope. The sensor is flexible (10% strain), compact, and does not require external reference equipment. The sensor is able to bend in 180 degrees in all directions, produces two-axis outputs that are linear up to 120 degrees of bending and has a response time less than 9 ms. This paper explores the use of the sensor for controlling the tip position of a robotic endoscope and detecting external forces. The design outlined in this paper has many possible applications in robotic endoscopes, surgical tools, snake-like robots and soft material robotics.