Soft robotic manipulators are continuum robots made of soft materials that undergo continuous elastic deformation and produce motion with a smooth backbone curve. In many applications, these manipulators offer significant advantages over traditional manipulators due to their ability to conform to their surroundings, and manipulate objects of widely varying size using whole arm manipulation. Theoretically, soft robots have infinite degrees of freedom (DOF), but the number of sensors and actuators are limited. Many DOFs of soft robots are not directly observable and/or controllable, complicating shape estimation and control. In this paper, we present three methods of shape sensing for soft robotic manipulators based on a geometrically exact mechanical model. The first method uses load cells mounted at the base of the manipulator, the second method makes use of cable encoders running through the length of the manipulator, and the third method uses inclinometers mounted at the end of each section of the manipulator. Simulation results show an endpoint localization error of less than 3% of manipulator length with typical sensors. The methods are validated experimentally on the OctArm VI manipulator.