Two non-linear bead and spring models are considered for the Brownian dynamics simulation of the behaviour of polymer chains in a dilute solution under shear or elongational flow. One of them is the HYBRID model whose springs are Hookean at low elongation, and beyond some spring length they follow a Morse potential with a given dissociation energy. This model is suitable for studying polymer fracture in strong flows. In this paper we describe the model and check that it has the proper behaviour in the two regions. The second model is a chain of finitely extensible, non-linear elastic (FENE) springs. Our simulations show several features of the FENE model that agree well with observation. In shear flow, the deformation of the FENE chain at high shear rate deviates from the square law followed at low shear, in agreement with some experiments. The model also predicts the typical shear-thinning, non-Newtonian behaviour of the shear viscosity. In elongational flows, the variation of the chain properties with the elongation rate shows a rather sharp increase at some critical rate that is reminiscent of the so-called coil-stretch transition.