  The two-dimensional nonlinear problem of steady flow past a body submerged
beneath an elastic sheet is considered. The mathematical model is based on the
velocity potential theory with fully nonlinear boundary conditions on the fluid
boundary and on the elastic sheet, which are coupled throughout the numerical
procedure. The integral hodograph method is employed to derive the complex
velocity potential of the flow which contains the velocity magnitude on the
interface in explicit form. The coupled problem has been reduced to a system of
nonlinear equations with respect to the unknown magnitude of the velocity on
the interface, which is solved using a collocation method. Case studies are
undertaken for both subcritical and supercritical flow regimes. Results for
interface shape, bending moment and pressure distribution are presented for the
wide ranges of Froude numbers and depths of submergence. According to the
dispersion equation, two waves on the interface may exist. The first, longest
wave is that caused by gravity, and the second, shorter wave is that caused by
the elastic sheet. The obtained solution exhibits strongly nonlinear
interaction of these waves above the submerged body. It is found that near the
critical Froude number, there is a range of submergences in which the solution
does not converge.
