This study investigates the steady-state flow field in a circular tube filled with a viscous fluid expelled by a long gas bubble. We use a finite difference method (FDM) with successive over-relaxation (SOR) in the computation of the viscous fluid flows. All empirical deduced bubble profile is employed to simplify the complex computation of the interface shape between the gas and the viscous fluid, By varying the ratio of the bubble width to the diameter of the circular tube (lambda), the numerical simulation shows three fluid flow patterns: the complete bypass flow, the recirculation flow and the transient flow. The first two flow patterns of the viscous fluid are coincident with other researches. The transient flow pattern found in the present study shows a clear transition from the complete bypass flow to the recirculation flow, as well as the migration of the stagnation point. The results also clearly present the effects of the inertia force, which is represented by the Reynolds number (Re), on both the flow patterns and the vorticity distribution on the bubble interface. The flow at the rear part of the bubble with higher Reynolds number (i.e., 0 < Re <= 400) is a novel study in recent researches. (c) 2005 Elsevier Ltd. All rights reserved.