This article presents a non-destructive method, based on the response to free vibrations, which can be used with efficiency and reliability to determine the Young’s modulus of polymer composite materials reinforced with natural or synthetic fibers. The non-destructive tests are carried out by measuring the frequencies of bending free vibrations of cantilever beams with additional masses. By using inverse methods, the experimental values of elasticity modulus E are assessed and validated by numerical simulation, using the finite element method (FEM). For FEM modeling, the materials are considered linear, homogeneous, isotropic, and viscoelastic.