The approach to numerical modeling of fiber reinforced concrete slab (FRCS) under blast load is considered. The slab is used for coverings of buried protective structures. The stress-strain state of this structure is investigated in the dynamic setting. The loads in this case change in time in terms of both intensity and area. The calculation makes provision for the consideration of rigid and deformable structure of support units. The damping properties of the structure are evaluated for its resistance to progressive collapse. Concrete dilatation and softening are factored in the numerical simulation. The bond between the fiber concrete and the reinforcement was modeled by introducing interpolation elements that simulate the absence of deformation in the area of their contact. The interaction of FRCS with the deformed support was modeled using the linear contact. The transition from the elastic-plastic deformation stage to the rigid stage was performed by introducing gap elements. The geometric nonlinearity, as well as the physical nonlinearity for fiber-reinforced concrete and reinforcement, was taken into account in estimating the ultimate loading. The load absorbed by the structure through the thickness of the ground during detonation explosion of a charge on its surface was considered. To realize numerical integration of the system motion equations, an implicit scheme was used. It is based on a modification of the Newmark step method in which effective matrices of fiber concrete and reinforcement stiffness are constructed at each step considering the loading history of the structure for its deformed state. The possibility of effective regulation of the stress-strain state of FRCS was established, which allows the design of effective and safe structures of this type.