The novelty of this paper is the use of two variable refined plate theory for free vibration analysis of plate. Unlike any other theory, the theory is variationally consistent and gives two governing equations, which are only inertially coupled and there is no elastic coupling at all. Number of unknown functions involved is only two, as against three in case of Mindlin's theory. The theory has strong similarity with classical plate theory in many aspects. The theory does not require shear correction factor and transverse shear stress variation is parabolic across the thickness. Simple variant of the theory is also presented.