Agricultural topsoils are characterized by a heterogeneous mixture of structural units with a considerable difference in soil mechanical properties. Mechanistic modeling of compaction for this layer is challenging because of the need to parameterize model input parameters. This study quantified soil deformation during loading in semi-confined conditions and searched for drivers decisive for observed strains with no a priori assumptions of material properties. Undisturbed soil samples were collected in the plough layer of eleven sandy and loamy soils in Denmark. The samples were adjusted to either of the following matric potentials: − 30, − 50, − 75, − 100, − 160 and − 300 hPa (pF from ∼1.5 to ∼2.5). Cores at each water condition were loaded with an annulus covering one third of the soil surface at either of the following normal loads: 30, 60, 90, 120, 150, 180 kPa. Multiple regression was performed to estimate the best model describing the variation in soil compressibility. Measured strain, ε, decreased with increase in soil organic matter, bulk density and pF, but the effect of pF was affected by soil clay content. The model explained ∼84 % of the variation in data and predicted well measured strain for two independent data sets. The regression model is suggested for prediction of soil deformation of arable topsoils in field traffic. A procedure is described for the prediction, including calculation of the relevant stress based on loading characteristics.