Abstract: In this paper, we propose and investigate a new approach to modeling variable curvature continuum robot sections, based on Euler spirals. Euler Spirals, also termed Clothoids, or Cornu Spirals, are those curves in which the curvature increases linearly with their arc length. In this work, Euler spirals are applied to the kinematic modeling of continuum robots for the first time. The approach was evaluated using the sections of numerous continuum robots, including two parallel continuum robots. Each robot consists of three parallel sections, each with three thin, long McKibben actuators. These sections are poorly modeled by the widely used constant curvature kinematic model. The constant curvature and Euler spiral models were compared and the Euler Spiral method was seen to be a significantly better match for a wide range of configurations of the robot hardware.