In this contribution, flexural vibrations of linear elastic laminates composed of thick orthotropic layers, such as cross-laminated timber, are addressed. For efficient computation, an equivalent single-layer plate theory with eight kinematic degrees of freedom is derived, both in terms of equations of motion at the continuum level and in terms of a finite element representation. The validity of the plate theory is demonstrated by comparing natural frequencies of a simply supported plate over a wide frequency range for which an analytical solution is available. Furthermore, the influence of individual material properties on the accuracy of the plate theory is investigated, demonstrating its broad applicability. The influence of material orientation on the accuracy of the plate theory is examined by comparative finite element simulations. It is shown that, for cross-ply laminates, the plate theory is valid for elements oriented at any angle to the material principal axes.