A bead and spring model is considered for the Brownian dynamics simulation of the behavior of regular star polymer chains in a dilute solution under both shear flow and extensional (or elongational) flow. Finite extensibility, excluded volume, and hydrodynamic interaction are taken into account to make the polymer model as realistic as possible. The behavior of star-like chains in flow is similar to that of linear and ring polymers. Thus, dependence of a given property with the arm molecular weight is analogous to that found for linear polymers when using the total molecular weight. In shear flow, the deformation of the chain and the shear rate viscosity dependence (the flow curve), are studied. We find a slope for the shear-thinning region of the flow curve close to -2/3. In elongational flow the coil-stretch transition is characterized by giving the relationship between the critical elongational rate and the arm molecular weight, which turns out to be similar to the power law found in linear chains. (c) 2005 Elsevier Ltd. All rights reserved.