The two-dimensional problem of determining the steady-state field of enforced joint gravitational motions of incompressible fluid and a round elastic plate covering its surface has been considered. The motions are caused by a point load moving periodically along the outer surface of the plate, and refer to enforced harmonic oscillations in the system. A procedure for constructing an exact analytical representation of the vibrational field of the plate’s bending displacements was proposed. The unwanted mechanical resonance conditions were formulated. The results obtained make it possible to find bending moments and shear forces, if need be, in assessment of the strength of a plate. Moreover, they may be useful, for instance, in organizing safe regular movement of vehicles on a layer of ice covering a body of water.