This paper describes the measurement of average strain, strain distribution and vibration of a cantilever beam made of Carbon Fiber Reinforced Plastics (CFRP), using a single Fibre Bragg Grating (FBG) sensor mounted on the beam surface. Average strain is determined from the displacement of the peak wavelength of reflected spectrum from the FBG sensor. Two unstrained reference FBG sensors were used to compensate for temperature drift. Measured strains agree with those measured by a resistance foil strain gauge attached to the sample. Stress distributions are measured by monitoring the variation in the full width at half maximum (FWHM) values of the reflected spectrum, using a proposed optical analytical model, described in the paper. FWHM values were measured for both the cantilever test beam and for a reference beam, loaded using a four-point bending rig. The trend of the stress distribution for the test beam matches with our analytical model, however with a relatively large noise present in the experimentally determined data. The vibration of a cantilever beam was measured by temporal analysis of the peak reflection wavelength. This technique is very stable as measurements are not affected by variations in the signal amplitude. Finally an application of FBG sensors for damage detection of CFRP plates, by measuring the natural frequency, is demonstrated. With small defects of different sizes applied to the CFRP plate, the natural frequency decreased with damage size.