A numerical study (taking into account inertial -, viscous - and pressure forces) has been made of eccentric core-annular flow through a horizontal pipe, special attention being paid to the vertical force on the core. The viscosity of the core is assumed to be so large that it behaves as a rigid solid. A wave is present at its surface. The shape of the wave is based on experimental results published earlier in the open literature. Due to the eccentricity the centre line of the core is shifted in the upward vertical direction with respect to the centre line of the tube. The vertical force on the core was found to be dependent on the Reynolds number: at small values of the Reynolds number the force is in the upward vertical direction, at large values the force is downward. This means that at large values of the Reynolds number an upward buoyancy force on the core due to a density difference between core and annulus can be counterbalanced. So a stationary core-annular flow is then possible. (C) 2012 Elsevier Ltd. All rights reserved.