The behaviour of mechanical structures in low frequencies is strongly affected by the existence of the boundary conditions. It is not usually possible to provide ideal boundary conditions, i.e. simply supported or clamped, for structures. Therefore the real structures are mostly constrained by elastic supports. Constructing an accurate mathematical or numerical model for a structure requires the knowledge of the support parameters. In this paper, a new method is proposed for the parameter identification of a rectangular plate constrained by elastic support. The method relies on the free vibration solution of the plate dynamics subjected to elastic boundary conditions and employs the optimization toolbox of MATLAB.