This paper presents the research of processes of high-speed impact of strikers with steel armor plates in a range 2100-4000 km/s for the purpose of specification of scientific conception about behavior of substances in extreme conditions and reception of more correct mathematical models describing deformation and destruction of media of difficult structure in the field of big nonlinear elastoplastic deformations. The impact of the compound strikers containing tungsten-nickel cores with steel barriers of various thicknesses is discussed. The strikers were accelerated in ballistic trunk-jet installation with the attached charge in caliber of 30 mm. The mathematical model of dynamics of high-speed deformation and destruction of solids is described. As a result of the experiment-calculated analysis the data about durability of barriers and its overcoming by increase of impact speed are obtained.