Dissipative particle dynamics (DPD) is a method for simulating complex fluid flows and other, colloidal phenomena. It is a mesoscopic method, in that it does not rely on a continuum-level description of matter, but nor does it completely capture molecular-level detail. As such, it offers the possibility of capturing some degree of molecular-level detail, while conforming to continuum hydrodynamics at larger length scales. We have tested the applicability of DPD to finite-Reynolds-number flows by studying a series of model problems involving flow around spheres and cylinders. Our study is the first to consider explicitly the effect of finite inertia in DPD simulations. Both flow around immobile objects and the translation and rotation of mobile objects are considered. For our test problems, we show that under computationally feasible conditions DPD simulations are quantitatively accurate up to Reynolds numbers of 50-100. Typically the physical cause of inaccuracies at higher Reynolds numbers is the onset of compressibility effects, which can be anticipated by making reference to a DPD Mach number. In addition, in our implementation of DPD, some new methods are introduced that result in the computation time scaling linearly with the number of DPD particles. It is also shown that improvements in accuracy can be realized by making use of the specular reflection boundary condition at solid-fluid interfaces. (C) 2004 Elsevier Ltd. All rights reserved.