Curvature sensitive CO2-laser induced long-period fiber gratings (LPGs) were employed to measure the Young's moduli of materials. Two techniques, 'bar resonance' and 'through transmission', were used. In the first case, flexural vibrations of bars made of various industrial materials arranged in a cantilever configuration were probed by the LPG. The measured response allowed us to obtain the bar's vertical movement as a function of time, its frequency components and the bar material's Young's modulus. In the second case, the optical response of LPGs was used to determine the propagation velocities of perturbations along a bar, which allowed the straightforward calculation of the Young's modulus. The values obtained show good agreement with the ones reported in the literature. The results obtained in this paper demonstrate the feasibility of using LPGs to dynamically characterize a material's elastic properties. To the best of our knowledge, this is the first demonstration of the use of long-period fiber gratings for dynamically determining Young's modulus values.