Dispersion of elastic waves in a bonded plate has been analyzed using the exact solution as well as by two approximate models: a spring model that neglects the inertia effects and a density model that does not account for the finite stiffness of the bond layer. It is shown that the two model predictions agree with the exact solution in two overlapped regions of the density and stiffness ratios. However, they fail to predict the actual behavior in certain regions of the parameter domain.