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The application of the method of boundary integral equations is considered for studying the stress state of flat viscoelastic bodies with inclusions. The method is based on the use of complex potentials and the apparatus of generalized functions. An analytical solution of the problem is obtained for a half-plane with inclusions of arbitrary shape. For a numerical study of the change in the stress state depending on the time and geometry of the inclusions, a discrete analogue of the system of boundary-time integral equations has been developed.

An approach for approximating unknown densities of potentials in the study of the stressed state of a flat viscoelastic piecewise homogeneous body with inclusions, bounded by piecewise smooth contours, is proposed. The method is based on the construction of a system of boundary-time integral equations to determine the unknown densities of potentials along the contours of the inclusions. The approximation of the unknown densities of potentials was performed taking into account the singularity of the stressed state of a flat viscoelastic body near the angular point of the dividing line of the regions.

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