In the present work the turbulent flow past a circular cylinder (Re = 3900) was computed by large eddy simulation (LES). The objective was not to investigate the physical phenomena of this flow in detail but to study numerical as well as modeling aspects which influence the quality of LES solutions. Concerning the numerical method the most important component is the discretization of the non-linear convective fluxes. Five different schemes were investigated. Moreover, the influence of different grid resolutions was examined. On the modeling side two aspects play an important role, namely the near-wall model and the subgrid scale (SGS) model. Owing to the restriction to a low Reynolds number in this study, no-slip boundary conditions were used at solid walls. Hence only the second aspect was taken into account. Two different subgrid scale models (Smagorinsky and dynamic model) were applied. Additionally, LES computations without any subgrid scale modeling were carried out in order to prove the performance of the above mentioned SGS models.