The objective of the work described in this thesis is the development of a configuration estimation scheme for quasi soft-bodied robots, with the end goal being accurate soft-robot proprioception to enable robotic manipulation of unknown external loads. The first chapter introduces the problem and state-of-the-art modeling methods. The second chapter presents work we did building on previous research on a novel sensing scheme for soft-bodied robotic configuration estimation. The third chapter discusses the development of a geometric shape-sensing model based on overlapping tendon-length measurements. This model is geometrically exact for a body composed of two constant curvature segments in bending. The next chapter discusses our implemention of this model on a real world system and tested in two and three dimensions. We estimated the shape of a 215 mm long robotic segment with less then 3 mm of median error for a set of 50 configurations causing motion in two dimensions and approximately 27 mm of median translational error in three dimensions. The final chapter draws conclusions and proposes future work to allow for full robotic proprioception.