Squeezing of a droplet between a pair of plates serves as an experimental method for probing the dynamics of moving contact lines (CL). It is also indicative of a possible interplay between inner-scale effects and the bulk flow hydrodynamics. In this paper strong squeezing of a two-dimensional liquid droplet between parallel plates moving against each other is studied in the inertialess approximation. It is shown that the dynamics of the moving CL is mainly governed by the macroscopic bulk flow, whereas molecular slip and wetting in the vicinity of the CL have a minor effect. As a result, the apparent contact angle continuously increases, and after some time rolling motion inevitably sets in. After a longer time, the shape of the free surface tends to become close to circular, albeit distinct from a circle. This is because at the late stage of squeezing, the shape of the free surface is determined mainly by the viscous stresses, which dominate capillary stresses due to the surface tension. (C) 2002 Elsevier Science Ltd. All rights reserved.