The author has previously derived an effective‐stiffness velocity‐corrected theory of laminated composite plates based upon a microstructure plate theory developed by C. T. Sun. The velocity‐corrected effectivestiffness plate theory is now used to study the flexural and extensional vibrations of simply supported rectangular plates; comparisons are made to similar results obtained from a reduced effective modulus or transversely isotropic plate theory. In each instance, free vibrations are assumed and a corresponding set of dimensionless differential equations and boundary conditions is found. Frequency equations for simply supported edges are developed by passing solutions harmonic in both length and width through the differential equations while at the same time automatically‐satisfying the boundary conditions for simple supports. The variation of dimensionless frequency for such dimensionless variables as number of layer pairs, width‐to‐thickness ratio, elastic ratio, width‐to‐length ratio, thickness ratio, and density ratio is presented graphically and discussed in detail. Also, comparisons of the effective stiffness and effective modulus frequencies are made for each of the varied dimensionless parameters.