The article presents a model of non-hydration hardening of dispersed systems - mineral binders (without the stage of hydration) and the results of studies of gypsum stone with ash filler from the standpoint of the formation of the optimal structure of the material of non-hydration hardening, as well as its density and strength. The model assumes the use of binary mixtures of dispersed components with different dispersions. The study was based on data on the granulometric composition and dispersion of gypsum powders and aluminosilicate microspheres. It was isolated from the ash-slag mixture - waste from a thermal power plant. The aluminosilicate microsphere contains not only microsized spherical particles of the amorphous phase but also nanosized grains in a sufficient amount. This makes it possible to control the particle packing density. Experimental verification of the optimization of the granulometric composition of a binary dispersed system based on gypsum and ash microspheres was carried out. Based on the results, the optimal content of the filler in the composition of the non-hydration hardening structure was established. It is shown that filling with highly dispersed particles affects the performance properties of the resulting modified stone.