Abstract The plane problem of hydroelasticity on the stability of a hinge-supported plate of infinite span placed in a rigid screen is considered in the case of unilateral flow of an ideal incompressible fluid. An analytical representation is obtained for the matrix elements of the averaged aero-dynamic loads. The possibility of using the method reduction in the problem under consideration, i.e., of replacing the infinite determinant by a truncated determinant is investigated. Relations are obtained for the flutter velocity as a function of the hydroelasticity and axial force parameters. The problem under consideration was solved in /1–3/ by different methods, where, by assuming the convergence of the infinite determinant to which application of the Bubnov-Galerkin method leads, consideration was confined to two coordinate functions and the forces acting on the fluid side were determined numerically. Only the boundary of the static stability domain was found.