A numerical study has been made of horizontal core-annular flow: the flow of a high-viscosity liquid core surrounded by a low-viscosity liquid annular layer through a horizontal pipe. Special attention is paid to the question how the buoyancy force on the core, caused by a density difference between the core and the annular layer, is counterbalanced. The volume-of-fluid method is used to calculate the velocities and pressures in the two liquids. At the start of the calculation the core is in a concentric position. Thereafter the core starts to rise under the influence of buoyancy until it reaches an eccentric equilibrium position where the buoyancy force is counterbalanced by hydrodynamic forces generated by the movement of a wave at the core-annular interface with respect to the pipe wall. At high Reynolds number of the flow in the annular layer core levitation is due to inertial forces, whereas at low Reynolds number viscous (lubrication) forces are responsible for levitation. We carried out two types of calculation. In the first we assume the interface to be smooth (without wave) at the start of the calculation and study how the wave develops during the rising period of the core. In the second a wave is already present at the start of the calculation.