The evolution of the withdrawal through a line sink of an initially quiescent, linearly stratified fluid in a semi‐infinite, horizontal duct is investigated. It is shown that due to the shear present in the withdrawal layer the previously suggested mechanism for the control of the higher mode shear fronts, which assumes that the velocity of the fronts is balanced by the oncoming flow, cannot occur. An alternative mechanism for the control of this flow is proposed based on solutions for the vertical structure of linear, long, internal waves in horizontal shear. This results in a model for unsteady selective withdrawal in agreement with steady‐state solutions. ©1995 American Institute of Physics.