This article presents the results of a study of the physical and mechanical properties of fine-grained fly ash concrete based on a combined reinforcement with steel and basalt fibers. The main studies were conducted using mathematical planning of experiments, which allowed the experiments to be algorithmized in terms of both the amount of experimental work and statistical requirements. Quantitative dependences characterizing the effect of the content of cement, fly ash binder, steel, and basalt fiber on the compressive strength and tensile splitting strength of fiber-reinforced concrete were obtained. It has been shown that the use of fiber can increase the efficiency factor of dispersed reinforcement (the tensile splitting strength to compressive strength ratio). To increase the resistance of basalt fiber, it is proposed to use fly ash in cement systems, which reduces the amount of free lime in the hydrating cement environment.