This paper details an investigation of the response spectra of an FBG sensor embedded in a cylindrical hollow composite beam which is subjected to pure torsion and torsion - bending combined loading. The spectra of embedded FBG sensors under torsional and combined loading were obtained and post processed in order to investigate the performances of FBG sensors in torsional strain measurements. Further, the spectra of the embedded FBGs located at the vicinity of the points of damage inside the tube were also investigated to identify the spectral changes due to the damage. A detailed finite element mesh was created for the hollow beam specimen and static analysis was performed for comparison. It has been found that the FEA results are in good agreement with the experimental results. Further, it has been observed that the reflected spectrums of FBG sensors were chirped due to a possible warping of the FBG sensor due to torsional loading.