The system for predicting tyre performance on sand, measuring sand strength with a cone penetrometer and using non-dimensional empirical curves developed by the Waterways Experiment Station (WES) of the U. S. Army was investigated. A series of tyre tests on dry Cresswell sand were carried out and the results were in complete disagreement with the WES system, in both its original and revised forms. It was therefore decided to try to discover the basic soil mechanics of such a system and modify it accordingly. Critical State Soil Mechanics describes two types of soil behaviour, dilating and weakening or compacting and strengthening. It was found that the first of these processes occurred in most situations likely to be found naturally, compaction occurring only in the loosest states obtainable under laboratory conditions. Under dilating conditions sand strength is described by the density, γ (Gamma). and the angle of internal friction, Ø. The angle of friction, for a single sand, was found to vary over a very wide range, depending on the state of compaction and the confining pressure. Density does not vary greatly. The cone penetrometer gradient, G, was found to be related to Ø at a low confining pressure, and the relationship was well described by the theory of Durgunoglu and Mitchell (1975). This lead to the idea that tractive performance would be dependent on Ø, which would be lower the higher the tyre contact pressure. A series of tyre tests on a single tyre on two sands showed clearly that performance depended on both tyre pressure and tyre load. The WES numeric only contains pressure. It was therefore decided to include both parameters by expressing performance by several curves depending on the tyre deflection. Deflection. being expressed as a ratio of tyre diameter rather than tyre section height. The new system was shown to describe all of the WES data better and more logically than their system. The reason why the system cannot describe performance in Yuma and Mortar sands with the same single curve as for Leighton Buzzard and Cresswell remains a mystery.