Estimating soil properties from the mechanical reaction to a displacement is a common strategy, used not only in in situ soil characterization (e.g., pressuremeter and dilatometer tests) but also by biological organisms (e.g., roots, earthworms, razor clams), which sense stresses to explore the subsurface. Still, the absence of analytical solutions to predict the stress and deformation fields around cavities subject to geostatic stress, has prevented the development of characterization methods that resemble the strategies adopted by nature. We use the finite element method (FEM) to model the displacement-controlled expansion of cavities under a wide range of stress conditions and soil properties. The radial stress distribution at the cavity wall during expansion is extracted. Then, methods are proposed to prepare, transform and use such stress distributions to back-calculate the far field stresses and the mechanical parameters of the material around the cavity (Mohr-Coulomb friction angle ϕ, Young’s modulus E). Results show that: (i) The initial stress distribution around the cavity can be fitted to a sum of cosines to estimate the far field stresses; (ii) By encoding the stress distribution as intensity images, in addition to certain scalar parameters, convolutional neural networks can consistently and accurately back-calculate the friction angle and Young’s modulus of the soil.