The influence of siliceous fly ash properties and conditions of maturation on compressive strength of fly ash concretes was studied in the paper. Moreover, a lot of strength models of fly ash concretes were analyzed in the paper. The analyses made on the basis research program. The partial replacement of cement by fly ash (0, 20, 35, 50% mass of cement), the coefficient w/s = 0,55; 0,45; 0,38, and kind of siliceous fly ash in three categories of losses of ignition A, B and C were variable in concrete mixes. A new model of compressive strength for fly ash concretes, build on the basis of research program is presented in the paper.