Over the years, many shape sensing methods have been developed with technologies including optical fibre, PZT and fringe projection. Among them, optical fibres have gained a lot of attention due to their unobtrusive nature when either surface mounted or embedded in the structure. Optical fibre Bragg gratings (FBG) are currently employed for structural health monitoring in civil and aerospace systems and their shape sensing capabilities have been previously reported. In this paper, we propose a novel fibre optic based shape sensor of an isotropic cantilever beam based on the principles of interferometry and FBG sensing. The method described in this paper uses a standard single core single-mode optical fibre and the least number of sensors to estimate the shape, making it comparatively an inexpensive sensing method. On displacing the beam with an unknown magnitude and at an unknown location along the beam, we are able to demonstrate that we can measure the shape of the displaced beam and the magnitude and location of the force applied. The analysis involves using a calibration method and an iterative calculation to measure the two unknowns. An analytical model based on the known beam theories was used to assess the accuracy of the measurements. The preliminary analysis yielded an accuracy of ±1 mm and ±50 mm for the displacement and location, respectively.