Society calls for protection of agricultural soils in order to sustain the production of foods for a growing population. Compaction of subsoil layers is an increasing problem in modern agriculture and a cause of serious concern because of the poor resilience in natural amelioration. The concept of soil precompression stress has been adapted from civil engineering, although in soil science it is applied to unsaturated soils that have developed a secondary structure from the action of weather, biota and tillage. It assumes strain is elastic at loads up to the precompression stress, while plastic deformation is expected at higher stresses. To determine this threshold we performed uniaxial, confined compression tests for a total of 584 minimally disturbed soil cores sampled at three subsoil layers on nine Danish soils ranging in clay content from 0.02 to 0.38 kg kg−1. The cores were drained to either of three matric potentials (−50, −100 or − 300 hPa) prior to loading. Stress was applied by a constant-strain rate method. We estimated the point of maximum curvature of the strain-log10(normal stress) relation by a numerical procedure. This point is considered here as a compactive stress threshold, typically labeled the soil precompression stress, σpc. The preload suction stress (PSS) was calculated as the product of initial (i.e., before loading) water suction and initial degree of pore water saturation. Multiple regressions were performed to evaluate the effect of soil properties (textural classes, volumetric water content, bulk density (BD), soil organic matter (SOM), and PSS) on σpc. The best model explained 39% of the variation in σpc, and indicated that σpc increases with increasing PSS, BD and SOM. For a given combination of clay, BD and SOM, PSS affected σpc negatively. We recommend our regression model for use in risk assessment tools for estimating sustainable traffic on agricultural soils. The model was validated by five independent data sets from the literature. Our study shows that caution should be applied when regarding σpc as a fixed threshold for compressive strength. We hypothesize that plastic deformation is initiated over a range of stress rather than at a distinctive single value. Further studies are needed to better understand—and potentially quantify—to what extent the predicted σpc can be regarded a central estimate of allowable stress for a given soil.