Empirical consistometry and slump tests can become true rheometrical tests when basic constitutive equation parameters can be calculated from experimental data files. One-dimensional formulas have been obtained successively within the two complementary frameworks of solid mechanics plasticity theory which is fit for moderate slump values, and that of fluid mechanics shallow-water theory, fit for significant spreading. They relate the slump value and/or the spreading radius to the dimensionless ratio of the shear yield stress s and the compression stress pgH at :he basis of the cylinder which was initially released. The influence of the aspect ratio H/2R and flat of the extensional stresses have been taken into account. Both are noticeable. The overall slump regime is found to have good potential as a theometrical test because the shape of the sample at rest depends only on its volume, not on any other geometrical property. Flow smoothes imperfections which may become more or less disturbing during the other regimes. A discussion of the two theories and comparison with experimental data enables a third matched theory to be suggested and the free surfaces obtained to be modeled over the whole range of relative yield stresses and sample volumes. (c) 2005 The Society of Rheology.