The restart of a pipeline containing gelled waxy crude oil after shutdown is simulated using a two-fluid displacement model. The model assumes that the gelled oil is to be displaced by pumping in another fluid under constant pressure and that the incoming fluid displays Bingham plastic behaviour. The theological behaviour of the gelled oil is characterised by a time-dependent constitutive equation with a yield stress, based on modelling of a North Sea waxy crude oil. The start-up flow model takes into account the compressibility and longitudinal variations in physical and theological properties of both fluids as they flow along the pipeline. The effects of yield stress and the compressible nature of the gelled oil are effectively handled by introducing the concept of a propagating yield front and initial compression flow, that precede viscous flow of the gelled oil for a successful start-up. The model predicts that start-up flow is subjected to two delay times, one due to the transient yield stress behaviour of the gelled oil and the other due to the compressibility effects. Oil compressibility has a positive effect on flow rate, movement of the fluid-oil interface and the time taken to clear the gelled oil from the pipe. The effects of other factors such as start-up pressure, initial compression time and liquid hold-up on flow after restart are also examined. The model produces a more realistic prediction of the start-up situation than a previous model developed for incompressible fluids. (C) 2004 Elsevier B.V. All rights reserved.