Improving the prediction accuracy of the risk of soil structure deformation during wheeling requires a better understanding of the effects of traction on the vertical and horizontal stress distributions beneath tyres. In this study, these distributions were assessed for a rear wheel of a pulled (i.e., passive) and pulling (i.e., active) tractor during wheeling. The total load of the tractor was 85.2 kN, with a static rear wheel load of 33.0 kN on a 650/60 R38-tyre, inflated to 80 kPa. The 4WD was disabled in the active configuration. Vertical and horizontal contact stresses were measured at a frequency of 1 kHz using pressure transducers at 0.10 m depth of a sandy loam agricultural soil, covering a width of about 0.75 m, thereby capturing the entire stress distribution beneath the tyre. With these data, the contact characteristics (apparent wheel load, contact area, mean ground pressure) were calculated, the stress distributions characterised, and the ratio of horizontal to vertical stress for numerous positions beneath the rear tyre obtained. The results show that traction modifies the tyre-soil interaction significantly. The tyre-soil contact area was larger and the magnitude of vertical stress was lower for the active than for the passive tyre. On the other hand, the magnitude of horizontal stress was higher for the active than for the passive tyre. Consequently, the ratio of horizontal over vertical stress was higher beneath the active than beneath the passive tyre (P < 0.001), with median values of 1.0 and 0.5, respectively. Vertical and horizontal stress peak values did not spatially align but occurred in different positions beneath the active tyre. These findings thus contradict the assumption that horizontal stress near the tyre-soil interface is simply a function of vertical stress. Traction changed the distribution of vertical stress at the tyre-soil interface, with vertical stress peaking in different positions beneath the tyres, whilst the effects of traction on the horizontal stress was primarily related to the magnitude. The results of this study highlight the importance of incorporating different drive modes in predictions of the stress-state beneath a tyre and thus the assessment of the risk of soil deformation induced by wheeling.