The dynamic processes for a mechanical system in the form of a gap between two vibrating rigid rectangular plates and filled fluid was studied. The gap wall were parallel to each other and have the same geometric dimensions. The bottom plate had an elastic suspension with a cubic nonlinear stiffness characteristic and can make longitudinal oscillations that were excited by periodic motion of the opposite one via fluid layer between them. For the gap under consideration, a plane hydroelasticity problem had set to study forced steady-state bottom plate oscillations. This problem includes the equations for Newtonian fluid and the gap wall. The system of equations was complemented by conditions at the cross-sections of gap ends for the pressure, as well as conditions for the velocities of fluid and rigid walls at their contact surfaces. The initial formulation of the gap wall hydroelasticity problem was simplified using the smallness transverse geometric dimension of the gap. The fluid velocity and pressure in the gap were determined, and the driving force for the bottom gap wall was found. The equation of longitudinal hydroelastic plate oscillations was obtained as a generalization of the Duffing equation. Based on the harmonic balance method, analytical expressions for the nonlinear response of the gap wall when considering pressure fluctuations at the ends and vibration of the opposite gap wall were determined. As a result, the responses of the gap wall caused by the longitudinal vibration of the opposite one were obtained and numerically investigated.