Non-recirculating and recirculating inertial flows of a viscoplastic fluid around a cylinder were studied numerically. The Herschel-Bulkley constitutive equation was considered. The flow morphology, the stress and pressure fields around the cylinder and the drag coefficient were determined over a wide range of Reynolds and Oldroyd numbers. The opposing effects of inertia and yield stress on the yielded zones and size of the vortices was demonstrated. Useful formulas in particular for the drag coefficient were also established for engineering purposes. The influence of the power law index was also studied for both shear-thinning and shear-thickening cases and this study revealed a complex behaviour. The position and size of the rigid zones as a function of the power law index and Oldroyd number are represented in different schemes. (C) 2012 Elsevier B.V. All rights reserved.