Extended layered structures are widely used as models of geological media in geophysics and seismology, soil foundations in foundation engineering, multilayer composites in materials science, etc. The presence of internal and interface defects in such structures changes their waveguide properties, affecting, among other things, their durability potential. When such structures are exposed to long-term vibrations of various origins (natural or manufactured), the presence of multiple thin stress concentrators can lead to localization of deformation processes. A wide range of vibration frequencies necessitates the development of effective methods for studying problems that describe oscillatory processes in structures with single and multiple defects. In this work, we present a method for studying and solving problems for layered materials with a single inclusion or with a system of inclusions under the influence of harmonic loads. The authors use the mathematical apparatus of the theory of vibration-strength viruses. To study the wave and stress fields caused by the vibration of the defect's edges and the surface emitters, we have obtained recurrent formulas for constructing Green's symbol matrices, which make it possible to write out systems of integral equations for the corresponding mixed problems. We have presented examples of solving integral equations for some plane and axisymmetric problems using the fictitious absorption method, which maintains high accuracy of the solution both at internal points of the region and near the boundaries in a wide range of frequencies.