This work provides a one-dimensional analytical theory for straight and axisymmetric consistometers, and helps with their use as rheometers. It is shown that these very economical and easy-to-use instruments provide an accurate characterisation of the theological behaviour of shear-thinning, shear thickening and other materials of high apparent viscosity. The study may also be used heuristically for other types of flow, such as geological flows. The theoretical problem considered here may be presented as that of the transient gravity flow resulting from the total, instantaneous failure of a straight or curved dam on a horizontal base. A succession of analytical solutions is found, depending on the time that has elapsed since the moment the flow was released. One of these, relating to the viscous slump of the entire fluid, is particularly pertinent for deducing measurements of the wave front progress or slump, the flow curve and the theological parameter values being involved in the mechanical behaviour of the material in question. Experiments conducted with a Newtonian glucose solution confirm the feasibility of rheometric characterisations and give rise to discussions on the range of validity of the theoretical predictions. (c) 2005 Elsevier B.V. All rights reserved.