Free vibrations of a transversely isotropic rectangular plate are investigated within the frameworks of the Timoshenko-Reissner (TR) model including a transversal shear. The dependence of the principal natural frequency on the shear parameter for various variants of boundary conditions is found. The generalized Kirchhoff-Love (GKL) model of fourth differential order for a multilayered plate is proposed. The GKL model is simpler than the TR model, and it gives the same results as the TR model in the most cases. This model is used to describe vibrations of multilayer graphene sheets (MLGS). Explicit formulas for principal frequencies for both multilayer ordinary plates and for MLGS are derived.