Core Ideas A new numerical method could detect the point of maximum curvature in the stress–strain relationship. The precompression stress identified by the new method correlated with the maximum stress the soil had experienced prior to the compression tests. The combination of soil water potential and bulk density had a larger influence on precompression stress than soil texture and soil structure alone. The concept of precompression stress is used for estimating soil strength that is relevant to field traffic. It represents the maximum stress experienced by the soil. The most recently developed fitting method to estimate precompression stress (Gompertz) is based on the assumption of an S‐shaped stress–strain curve, which is not always fulfilled. A new simple numerical method was developed to estimate precompression stress from stress–strain curves, based solely on the sharp bend on the stress–strain curve partitioning the curve into an elastic and a plastic section. Our study had three objectives: (i) assessing the utility of the numerical method by comparison with the Gompertz method, (ii) comparing the estimated precompression stress to the maximum preload of test samples, and (iii) determining the influence that soil type, bulk density, and soil water potential have on the estimated precompression stress. Stress–strain curves were obtained by performing uniaxial confined compression tests (UCCTs) on undisturbed soil cores for three soil types at three soil water potentials. The new method performed better than the Gompertz fitting method for estimating precompression stress. The values of precompression stress obtained from the new method were linearly related to the maximum stress experienced by the soil samples prior to the UCCT at each soil condition, with a slope close to 1. Precompression stress determined via the new method was not related to soil type or dry bulk density. This might because the range for both parameters was too small but it may also emphasize the complex effect of soil structure on soil mechanical strength.