An interferometric fiber optic sensor is used to monitor the vibration of a bar under tension. An analytical formula is derived to relate the density. Young modulus and the physical dimensions of the bar to its frequency of vibration, which is measured through FFT of the monitored signal from the fiber optic sensor. Bars made up of homogeneous materials are tested for the validity of the method, which is then applied to composite materials. In the latter application, an optical fiber, which form an integral part of the sensor, can be embedded into the bar during its fabrication process. For materials of stable moduli, the sensor can be used to measure the tension of the bar. For materials with unstable moduli, during its curing process, the aging period or otherwise, the sensor can be used to monitor the change. The method can also be used as an alternative to measure the moduli of materials and is especially suitable for composite materials. Due to the complexity of a composite material, the modulus measured by this method reflects an average effect of the bulk, whereas a conventional tensile test depends more on localized weaknesses of the composite.