The purpose of the numerical simulations carried out in this study is to determine the flow characteristics of a Herschel-Bulkley viscoplastic fluid around a cylinder in an infinite medium. Inertia is assumed to be negligible. Two types of boundary conditions are considered: the fluid adheres or slips (zero tangential stress) on the cylinder wall. Finite-element modelling involves regularising the Herschel-Bulkley model, as proposed by Papanastasiou [J. Rheol. 31 (1987) 385]. The effect of the yield stress value and shear-thinning index on the kinematic field and drag exerted on the cylinder were explored systematically. The location, dimension and kinematics of the rigid zones were determined. The results are compared with available theoretical data. (C) 2003 Elsevier B.V. All rights reserved.