For the simulation of stress waves in solid deformable bodies are used the equations of the mathematical theory of elasticity. The task is implemented using a numerical simulation of differential equations of the wave theory of elasticity. The problem is solved by the method of end-to-end account, without allocation of breaks.

Forecast security of unique structures that are in the air and solid deformable environment under wave impacts is determined using numerical simulation.

In [1-10] provides information on the mathematical modeling of various stress waves by means of the developed numerical method, algorithm and complex programmes in the areas of different shapes.

On the basis of the finite element method in displacements the developed method, algorithm and program complex for solving linear flat two-dimensional problems, which allow to solve complex problems under wave impacts on structures.

Solved the problem of propagation of unsteady elastic shock waves in a console with an elastic half-plane. The problem of impact of air shock waves on a console (the ratio of width to height of the console – one to two, four, six, eight and ten) with an elastic half-plane. The problem of horizontal concentrated impact of air shock wave on an elastic half-plane. The studied computational domain have 4008004 nodal points. Solves the system of equations from 16032016 unknown.

For an example of the results on the impact of air shock waves on a console (the ratio of width to height of the console – one to ten) with an elastic half-plane. Tensile elastic normal stress in the shell has the following maximum value . Elastic compressive normal stress in the shell has the following maximum value . Tensile elastic normal stress at the base of the console has the following maximum value . Elastic compressive normal stress at the base of the console has the following maximum value .

The results can be evaluated as a first approximation to the solution of complex problems about the impact of air shock wave on the console with an elastic half-plane, using numerical simulation of wave equations of the nonstationary theory of elasticity.

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