We use lubrication theory to study the bow-wave ahead of a squeegee as it moves steadily over a horizontal layer of fluid. If the squeegee is infinitely long with a small gap at its base then the motion is two-dimensional and we obtain an analytic prediction for the flow thickness. For a relatively long straight squeegee on a layer of viscous fluid with no gap, we deploy a two-dimensional approximation, which enables the flow thickness in the bow-wave to be determined relative to the thickness at the squeegee. The analysis is completed by balancing the flux into the bow-wave with the transverse flux perpendicular to the squeegee associated with hydrostatic pressure gradients. The simple method is adapted to squeegees that are angled to the direction of translation. For a layer of viscoplastic fluid that has a relatively high yield stress, the bow-wave is quasi-plugged and this observation enables a different flux balance to be used to determine the flow thickness. The predictions are compared favourably to numerical results.