Stationary wave motion in an unbounded fluid-loaded elastic sandwich plate of symmetric composition is considered in a three-dimensional problem formulation. Several alternative theories are suggested, including a formulation in the framework of a theory of elasticity applied for the core ply. In the first instance, a fluid loading at the both sides of a plate is considered and ?in-phase? and ?anti-phase? wave motions (with respect to transverse deflections of skins) are analysed independently upon each other. It is shown that the simplified models are capable to give a complete and accurate description of all propagating waves in not too high frequency range. Furthermore the analysis is extended to take into account for the ?symmetry- breaking? effects, e.g., a static pre-stress of one of skin plies and a fluid loading at one side of the sandwich plate. The standard perturbation technique is applied to analyse an interaction between dispersion curves.