Non-vesicular basaltic melts behave as Newtonian fluids at temperatures above their liquidus and their viscosities can be calculated using a method developed by Shaw (1972) and Bottinga and Weill (1972). Because many igneous processes involve the flow of silicates at sub-liquidus temperatures, numerous attempts have been made to calculate the interactive effects of the crystal phase. However, current methods are appropriate only for relatively low crystal concentrations, and they assume Newtonian behaviour; we argue that this assumption is invalid when bubble or crystal concentrations exceed 30%. At higher concentrations, factors other than concentration become increasingly important; these include particle shape and size distribution. A method which takes these factors into account is tested on a range of suspensions, including magmas at sub-liquidus temperatures, and rheological properties calculated using this method agree closely with the measured values. We also demonstrate that an equation which was introduced to explain large differences in measured apparent viscosities during the cooling and crystallisation of Mount St. Helens dacite (Murase et al., 1985), and which is currently used to calculate the rheological properties of crystallising lavas, generates viscosities which may be in error by several orders of magnitude. This difference is argued to be caused by a combination of factors, including the ten orders of magnitude range in the strain rates utilised during the Mount St. Helens measurements causing orders of magnitude difference in the resulting apparent viscosities. Rheological data on crystallising silicic melts are reinterpreted taking into account the non-Newtonian rheology of the magmas and changes in activation energy of flow during crystallisation.