A simplified simulation model is designed to investigate the vacuum-driven bonding of glass panels in the cell process for LCD manufacturing. The bonding process is modelled by the transient flow of a weakly-compressible fluid in a very thin channel between two horizontal glass panels. An order of magnitude scaling analysis is conducted based on the characteristic feature of the channel of which height is much smaller than the horizontal length scales. It is revealed that the flow in the channel is represented by a Poiseuille flow of a compressible fluid. A finite volume model has been constructed to acquire the numerical solution to the derived simplified equations. For a simple test problem of pressure-driven microchannel flow, an assessment is made of the accuracy and validity of the proposed model. The basic aspects of vacuum-driven bonding are examined numerically, and the applicability of the present simulation model is illustrated.