Article shows the typical examples of mathematical models realization of probabilistic description of random variables (RV) distribution of geotechnical characteristics and the heterogeneity parameters according to data of laboratory and field tests of compacted soils, mining industrial wastes and their mixtures. It also presents the variability of some technological parameters of soil cushions erection. The statistical parameters of RV distribution of designed and ultimate strengths of compacted soils, as well as settlement of foundations on cushions were determined by analytical methods. By means of numerical simulation of cushion tensely-deformed state (TDS) by method of ultimate elements (MUE) using the elastic plastic model, imitation simulation by Monte Carlo method and experimentally obtained distribution laws of RV of compacted soils characteristics, the statistic parameters and distribution laws of foundations settlements were obtained. Due to statistic analysis of settlements distribution of artificial foundations bases and their relative differential settlements the probability of failure was obtained.