The present paper describes two different nondestructive approaches for the direct identification of the elastic constants of thin square isotropic plates. First a static method is presented, by which the identification of the Young's modulus and Poisson's ratio is carried out by the full field measurement of the out-of-plane displacements detected on the upper surface of the plate in two biaxial bending tests. Then a dynamic method is illustrated, by which the elastic constants are determined from two different natural frequency of a free vibrating plate. Both techniques, previously verified on a carbon steel specimen, have been applied to a CVD diamond specimen; a comparison between the two approach is reported and the influence of the measurement errors is also discussed.