Bubbles in shear flows experience a lift force, causing them to migrate sideward while they are rising. This lateral migration is also observed in numerical simulations, which are carried out with an extended version of the highly parallelized code FS3D, employing an advanced Volume-of-Fluid method. The movement of single bubbles in linear shear flows is simulated to obtain the magnitude of the lift force – expressed by the lift force coefficient CL – for various bubble diameters and material data. Simulation results are in good agreement with experiments for medium liquid phase viscosities. The pressure and the velocity fields near the interface are investigated and the contribution of dynamic pressure and the circulation of the lift force are discussed.