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At the final state of the slump test for yield stress, an axisymmetric deposit of height $h(r)$ is just able to support itself. Hydrostatic pressure gives radial pressure gradient $\rho g{h}^{\prime }(r)$, while lubrication theory makes the magnitude of the basal shear stressThe marginally yielded final profile therefore satisfiesIntegration givesUsing mass conservation, the known volume isSolving for the yield stress produces the estimateThus one measures the final radius $R$ and inserts it with $V$ and $\rho$. The estimate assumes a thin deposit, negligible surface tension, complete initial yielding, and a spatially uniform yield stress.

Dry sand is a granular material governed primarily by frictional stability. Its final free surface reaches the angle of repose ${\theta }_r$, so the deposit is approximately a cone,This constant-slope profile differs from the square-root edge of the yield-stress-fluid model.

A slump test for yield stress probes a material by allowing a molded sample to deform under its own weight. Fill a known mold on a level support, remove the mold, and measure the decrease in height or the spread of the final deposit. Gravity supplies the driving stress; resistance associated with the yield stress can arrest the motion before the sample becomes a thin layer.

The measured distance is not itself a stress. Inferring yield stress requires a calibrated relation or a mechanical model using the initial geometry, final shape and density. The final slump alone generally cannot identify both yield stress and dynamic viscosity: a time-resolved measurement provides additional information. A modified concrete test, for example, records the time required for a specified fall as well as the final slump.^[ref] The procedure is useful as a simple field measurement, with interpretation dependent on sample history and geometry.