Keywords: dilute polymer solutions, FENE model, free surface flows, Finite Elements Abstract: The effects of polymer additives on the break-up of jets in continuous (CIJ) and drop on demand (DOD) inkjet printing are considered. In continuous inkjet printing the fluid jet is modulated at close to the Rayleigh frequency to produce a steady stream of uniform drops, while in drop on demand printing individual drops are generated by applying an impulse to the fluid. Even at very low concentrations the presence of high molecular weight polymers significantly affects how jets break-up into drops, due to the high extension-rates involved. By simulating these flows with the FENE dumbbell constitutive equation we are able to establish the parameter values controlling the break-up length and character of jet break-up, such as the production of small satellite droplets (which are detrimental to the inkjetting process). For the case of drop on demand printing, we compare our predictions to experimental measurements on dilute solutions of monodisperse polystyrene. By using Zimm theory to predict the parameter values in the FENE model, we are able to demonstrate quantitative agreement between simulations and experiments.