The conjugate problem of nonstationary motion of a flat plate in a medium has been formulated and solved with consideration of the structure formation processes in the context of the self-consistent nonlocal hydrodynamic approach developed previously in [1-5] for the description of fast processes in inhomogeneous media. An approximate analytical solution with a two-layer structure including a dynamic wall sublayer and a viscous boundary layer has been obtained. It is demonstrated that the growth of dissipative structures is initiated by considerable relative accelerations arising in the medium near the surface streamlined with high velocities. The structures formed in transition regimes influence significantly the characteristics of motion even in the quasistationary stage of the process [6]. © 2001 Plenum Publishing Corporation.