An inverse technique, based on the planning of experiments and response surface methodology have been applied to determine elastic properties of unidirectional carbon fiber composite plate and carbon nanotubes reinforced aluminium plate. The nuances of application of investigated technique for orthotropic material properties determination are considered on the example of a composite plate. In turn, possibility of using of this technique on specimens with small dimensions (80x60x2 mm) is checked up and estimated on an example of an isotropic nanocomposite plate. The results obtained were verified by comparing the experimentally measured eigenfrequencies with numerical ones obtained by FEM using determinated elastic material properties.