Refinements and generalizations are made to a method developed by the first author and associates to obtain the elastic constants of composite materials using data from vibration tests on freely-supported plates. Elastic constants identified from different sets of vibration model data varied in accuracy. In this work, sensitivity analysis is automatically integrated into the procedure. The flexibility of using diagonally symmetric modes (in the case of isotropic, square panels), omitted from previous models, is also provided. Accurate identification of Poisson ratio values has been one of the main challenges in this area of research. Attempt is made to refine the search procedure for these values. Different example cases are considered.