The flow around a stream-wise oscillating circular cylinder in a steady uniform flow is computed using large eddy simulations (LES). A finite volume method with capability to handle moving meshes is employed. The results are used for comparison with experiments for validation of the algorithms. Another goal of the investigation is to obtain information, complimentary to that of the experiments, about the process of vortex shedding, the structure of the flow in the wake and the relation between this and the forces acting on the cylinder.