A mathematical model is formulated for the partial evacuation of viscous fluid from a rectangular cavity by the action of a passing meniscus. This time-dependent free mathematical model is formulated for the partial evacuation of viscous fluid from a surface problem is of direct relevance to the direct gravure coating process. Evacuation from a rectangular cavity is considered by taking account of the motion of the dynamic contact line down a vertical side wall. A two-dimensional solution is obtained using a Lagrangian finite element method, and results reveal the effects due to cavity aspect ratio and fluid properties. It is concluded that the fraction of fluid evacuated increases as (i) the cavity aspect ratio (cavity width) increases and (ii) the Capillary number decreases-though for cavities with a larger aspect ratio evacuation is independent of Capillary number.