The motion of a gas-liquid interface in a cylindrical capillary was studied. Stream function and vorticity equations were set up to describe a two dimensional flow in the liquid phase. Only momentum transfer is of interest; no heat transfer and mass transfer are involved. The driving force for flow is the pressure in gas phase; the surface tension is assumed negligible . Numerical solutions were obtained for a few time steps. The deformation of interface and the pattern of stream lines have been plotted.