The theory of hydrodynamic squeeze-out of lubricant film confined between two surfaces was analyzed. Two dimensional Navier-Stokes equations with an interfacial friction term were solved combined with Monte Carlo simulations for the analysis. The squeeze-out of liquid was a result of the pressure gradient existing in the lubrication film in the contact area. Drift velocity was calculated analytically as a function of distance of the island to the periphery of the contact area. A stochastic numerical approach to solve the problems of moving boundaries causing thermal fluctuations was also presented.