The paper deals with a comparative study of LES and RANS (k-$\epsilon$ model) results for a typical bluff-body flow, namely the flow around a surface mounted cubical obstacle placed in a plane channel. For this test case detailed experimental data (Re=40,000) are available [11]. Two slightly different numerical solution procedures based on a 3-D finite-volume method are used in this investigation. The Reynolds-averaged equations for incompressible flow are solved implicitly [10], whereas in the LES code [1, 2, 3, 4, 5] an explicit second order Adams-Bashforth scheme is applied. Different formulations of the k-$\epsilon$ turbulence model are used in the RANS simulations, the standard version with wall functions, a RNG version, a modified version proposed by Kato and Launder [7], and a two-layer approach. For modeling the non-resolvable subgrid-scale motion in the LES two different models are applied, namely the well known Smagorinsky model [16] as well as the dynamic model originally proposed by Germano et al. [6]. The capability of the different methods is demonstrated by comparison with the measurements.