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The purpose of this paper is to investigate the problem of fracture of construction by solution of several mixed unsteady boundary value problems of elasticity, determination of stress intensity factors and concentration of stresses near edges of cracks and by numerical calculations of them obtained by explicit formulae.

The main methods of solution are integral transformations of Laplace and Fourier, method of Winner‐Hopf system solution by avoiding the singularities of coefficients of their matrices and factorization of them using numerical solution of the same order system of Fredholm integral equations. The solution for stresses is obtained in originals by effective Smirnov‐Sobolev form. The obtained integrals for stress intensity coefficients are calculated for considered cases of plane and anti‐plane problems of cracks, and for more complex space problem of crack are carried out all mentioned analytical investigations, including derivation of stresses distributions formulae near crack edge.

These analytic and numerical methods based on dynamic elasticity approximation on account of singularities near cracks edge allow precise calculation of the possibility and character of fracture of media under any loading of rather complex type.

Results can be useful for investigation of constructions responsibility. The developed mathematical methods are original and modern, using all actual effective methods of investigation of solutions of linear system of equations with three and four independent variables for complex initial, boundary value problems.