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The paper presents results of the research on strength of concrete slabs reinforced with steel fiber and tested under a high velocity impact. Mathematical models are proposed to describe the behavior of continua with a complex structure with consideration of porosity, non-elastic effects, phase transformations and dynamic destructions of friable and plastic materials under shock wave impact. The models that describe the behavior of structural materials were designed in the RANET-3 CAD software system. This allowed solving the tasks of hit and explosion in the full three-dimensional statement using finite elements method modified for dynamic problems. The research results demonstrate the validity of the proposed mathematical model to calculate stress-strain state and fracture of layered fiber concrete structures under high velocity impact caused by blast wave.