Shear flow over a finite compliant patch (bump or dip) in an otherwise fixed wall is considered here. This concerns unsteady flow in a channel, pipe or boundary layer, for two or three spatial dimensions. Applications in aerodynamics, sports, environment, biomedicine, drag reduction and flow-structure interactions form the background. Slowly evolving features are examined first to allow for variations in the incident flow. Linear and nonlinear analyses show that at certain parameter values (eigenvalues) resonances occur in which the interactive effect on flow and patch shape is enlarged by an order of magnitude. Similar findings apply to a boundary layer with several tiny patches present or to channel flows with patches of almost any length. These resonances lead on to fully nonlinear unsteady motion as a second stage, after some delay, combining with finite-time breakups to form a distinct path into transition of the flow.