The first five branches of the dispersion curves for straight‐crested waves propagating in an infinite isotropic elastic plate, in a state of plane strain, that is covered by a layer of an incompressible inviscid liquid are determined numerically from the exact dispersion relation. Using the classical theory of flexure, the Mindlin theory of flexure, and the Kane‐Mindlin theory of extensional motion in elastic plates, approximate dispersion relations are derived, and the effect of coupling between the flexural, extensional, and fluid modes is studied. Upon comparison of the exact and approximate results, it is found that the coupling of flexural and extensional motions arising through the velocity continuity condition at the liquid‐plate interface is rather weak, so that good approximations to the fluid, flexural, and thickness‐shear branches of the dispersion curves can be obtained by neglecting the coupling with the extensional and thickness‐stretch branches. Furthermore, the extensional branch is not appreciably influenced by the coupling condition, and the thickness‐stretch approximation is a good one in the low‐frequency range only if the mass density of the plate is much greater than that of the liquid.