The ability of a drop to stick to a solid surface is investigated when the surrounding fluid is in motion. The specific problem analysed consists of a small drop on a planar surface immersed in a second immiscible fluid which is flowing parallel to the solid surface at a constant rate of strain. An expression is obtained, in terms of experimentally measurable quantities, for the value of the rate of strain beyond which the drop cannot maintain contact with a fixed position on the solid. The most limiting restrictions assumed in the analysis are that both the advancing contact angle and the contact angle hysteresis must be small.