Selecting the appropriate tyre configuration and settings for heavy farm vehicles is important to ensure that soil compaction and power loss in rolling resistance are minimised and traction is optimised. This study investigated the effect of front-wheel assist (FWA, ≈75 kN) and four-wheel drive (4 WD, ≈100 kN) tractors fitted with different tyre configurations (single, dual), tyre sizes and inflation pressures on soil strength (a proxy for soil compaction), and rolling resistance. Single-pass tests were performed on a Typic Argiudoll (≈23% clay, bulk density: 1305 kg m−3) managed under permanent no-tillage. Results showed that average power losses in rolling resistance were 7.5 kN and 5 kN for the 4 WD and FWA tractors, respectively. The average rut depth increased by approximately 1.4 times after a pass of the 4 WD compared with the FWA tractor. The soil cone index (0–600 mm depth) increased from 2023 kPa (before traffic) to 2188 and 2435 kPa after single passes of the FWA and 4WD tractors, respectively (p < 0.05). At the centreline of the tyre rut, dual tyres reduced the soil cone index a little compared with single tyres, but they significantly increased the volume of soil over which soil strength, and therefore soil compaction, was increased. For both tractors (regardless of tyre configuration or settings), soil strength increased to the full measured depth (600 mm), but relative changes before vs. after traffic became progressively smaller with increased soil depth. The power loss in rolling resistance was consistently greater with the heavier tractor, and rut depth was directly related to tyre inflation pressure.