Some aspects of the free-vibration analysis of rigid rectangular ship structure plates are considered. In particular unusual mode shapes for square plates, to be derived in the FEM analysis of the problem, are explained by using superposition effect. The family of fundamental solutions of the biharmonic equation in free-vibration problem of rigid plates has been obtained. The solutions ware used for the mode shapes analysis of rectangular plates with hinged and clamped sides supports. For the case of fully clamped plates the approximate asymptotic solutions ware proposed too. Comparison of the results for fully clamped plates, derived by using FEM analysis and asymptotic solutions, displayed close results.