In vibration analysis of sandwich beam/plates, it is often assumed that there occurs shear deformation only, i.e. no extension or compression, in the core viscoelastic layer. Certainly, this assumption may have limitations, for example, with increase of the core thickness or frequency range of vibration. The purpose of this paper is to consider the extentional as well as shear strain of the core for modal parameter estimation of the sandwich plates and to investigate how much error will be caused by neglecting the extension or compression in the core material. Natural frequencies and modal loss factors are estimated for a simply supported square plates under each of the above two assumptions. Nondimensional characteristic equations are formulated and solved for various ratios of the base layer thickness to plate length, core to base layer thickness, and constraining layer to base layer thickness.