The use of fiber in cement materials is a promising and effective replacement for bar reinforcement. A wide range of fiber-reinforced concretes based on composite binders with increased impact strength characteristics have been developed. The synthesized composites included the composite binder made of Portland cement, silica, and carbonate additives. Basalt and steel were used as fibers. The nature of the influence of the composition and manufacturing technology of cement composites on the dynamic hardening coefficient has been established, while the growth of these indicators is achieved by creating a denser interfacial transition zone between the cement paste, aggregate, and fiber as a result of improving the homogeneity of the concrete mixture and controlling the consistency. Workability indicators (slump flow up to 730 mm; spreading time up to a diameter of 50 cm is up to 3 s) allow them to be classified as self-compacting concrete mixtures. An increase in the values of the impact strength coefficient by a factor of 5.5, the dynamic hardening coefficient by almost 70% as a result of interfacial interaction between fibers and binder matrix in the concrete composite, as well as absorption of impact energy by fiber, was revealed. The formula describing the effect of the loading rate on the coefficient of dynamic hardening of fiber-reinforced concrete has been refined. The fracture processes of the obtained materials have been established: after the initiation of primary cracks, the structure of the composite absorbs impact energy for a long time, while in the inelastic range (the onset of cracking and peak loads), a large number of secondary cracks appear.