Methods for strengthening soils under bases and foundations of buildings and structures with compaction of the base composed of weak mineral soils by determining the optimal design process parameters of the ground piles over the entire area of the base. The essence of the invention is that the method of compaction of bases composed of weak mineral soils that includes formation of a well, filling each well with the compacting material, and creation of a compacting effect on the compacting material by the hollow tubular working tool to form a ground pile. Preliminary engineering and geological surveys of the base area is performed to determine the values of the modulus of deformation, the Poisson's ratio, the internal friction angle, the specific cohesion, the specific gravity, and the initial void ratio of the weak mineral soil.