In a series of field experiments we measured the stresses in sand beneath single front and dual rear tyres of a John Deere 8300 tractor, using earth stress cells installed beneath the tyres. The stress in the sand increased both with increasing tyre inflation pressure (constant axle load) and with increasing axle load (constant tyre pressure).Analysis of the experiments using a finite element model showed that the stresses in the top 60 - 70 cm of soil depended mainly on the tyre / soil contact pressure; the influence of the lugs was particularly important. Stresses deeper than that depended mainly on the total load applied to the surface, increasing with increasing axle load.The model was used to simulate compaction in clay soils. Compaction predicted beneath the tyres depended on the strength of the soil, which in turn depends on the moisture content. However, tyre / soil contact pressure and axle load were still important.