Measurements of bubble rise velocities in two gas fluidised beds have been compared with numerical simulations of spherical bubble-wake regions rising through Newtonian liquids. The comparisons have been used to elucidate the theological nature of the dense phase of gas fluidised beds. The investigation sheds new light upon results obtained in the past by other workers, who did not have the benefit of the powerful numerical simulation techniques of today. It was found that the assumption of a Newtonian viscosity coefficient of 0.8 Pa s (values around this have often been suggested in the literature) yields bubble rise velocities of the right order of magnitude. Nevertheless, the experimentally determined variation in bubble rise velocity with size cannot be explained fully on basis of a Newtonian rheological model, but indicates shear-thickening behaviour of the dense phase. A discussion, also of the effect of bubble Reynolds number and wall effects upon the dense phase flowpattern around rising bubbles, and comparison with other work is provided.