A new model for long internal waves in a sheared flow with a critical layer near either lower or upper rigid boundary has been developed. In such system even small disturbances give rise to a formation of a zone filled with the mixed fluid. One nonlinear differential equation for the wave amplitude is derived in the steady case, in which the nonlinearity arises essentially due to the presence of the mixed zone. Solutions of the obtained equation include periodic waves on the induced mixed layer, a stationary bore and a combinational solution consisting of series of recirculation zones located alternatively near both boundaries.