A number of experimental investigations have been performed to study vibration characteristics of elastic plates in a high-frequency region. Up to this time the empirical data have no satisfactory explanation in terms of Lamb wave coupling. The theoretical analysis of the coupling effects presented in the article is based on the exact solution of the free-axis-symmetric vibration problem for a circular plate. Consideration of a special case of zero Poisson's ratio allows one to distinguish and investigate three independent kinds of eigenmodes. Two of them are initiated by simply propagated longitudinal waves. The waves with complex wave numbers (evanescent standing waves) provide a rise to a third type of eigenform. Eigenfrequencies of these last modes are very close to the thickness resonance frequency and they increase as radius of a plate increases. The data for nonzero Poisson's ratios demonstrate an influence of coupling on a structure of eigenfrequency spectra and mode shape. An investigation of radius variation effects gives a good indication of the feasibility of the coupling effect control. The values of the plate radius with the moderate mode shape disturbances are determined.