In the past, the analyses of floating ice plates subjected to static or dynamic loads were based on the theory of a thin homogeneous plate, although in actual floating ice plates Young's modulus may vary strongly with depth. Recently,A. Assur concluded, on the basis of a heuristic argument, that the solutions obtained for homogeneous plates may be used for floating ice plates, if a modified flexural rigidity is used. The purpose of the present paper is to study this question, by establishing a mathematically consistent formulation for the dynamic plate equation, utilizing Hamilton's Principle in conjunction with the three dimensional theory of elasticity. It is proven that for a variable Young's modulus and a constant Poisson's ratio the resulting formulations for plates and beams are the same as those for the corresponding homogeneous problems, if a modified flexural ridigity is used; thus confirmingAssur's conclusion. It is shown that the stress distribution is not linear and that the stress formula\(\sigma _{\max } = M{{z_0 } \mathord{\left/ {\vphantom {{z_0 } I}} \right. \kern-\nulldelimiterspace} I}\) used by a number of investigators for the determination of the carrying capacity of a floating ice plate, as well as for the computation of failure stresses from tests on floating ice beams, is not applicable. Correct formulas are derived, corresponding stress distributions are presented and the consequences of the findings discussed.