Bubbles in shear flows experience a lift force, causing them to migrate sideways while they are rising. This lateral migration is investigated 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. An investigation of the dynamic pressure on the bubble surface explains why large bubbles migrate in the opposite direction compared to small bubbles.