Structure and strength are responsible for soil physical properties. This paper determines in a uniaxial compression test the strength of artificial soils containing different proportions of various clay-size minerals (cementing agents) and silt-size feldspar/quartz (skeletal particles). A novel empirical model relating the maximum stress and the Young’s modulus to the mineral content basing on the Langmuir-type curve was proposed. By using mercury intrusion porosimetry (MIP), bulk density (BD), and scanning electron microscopy (SEM), structural parameters influencing the strength of the soils were estimated and related to mechanical parameters. Size and shape of particles are considered as primary factors responsible for soil strength. In our experiments, the soil strength depended primarily on the location of fine particles in respect to silt grains and then, on a mineral particle size. The surface fractal dimension of mineral particles played a role of a shape parameter governing soil strength. Soils containing minerals of higher surface fractal dimensions (rougher surfaces) were more mechanically resistant. The two latter findings appear to be recognized herein for the first time.