Methods of investigating boundary-value problems for bodies with crack-containing coatings are described. Coatings are simulated by plates of different types making contact with each other horizontally. The static boundary conditions that describe the vertical and horizontal effects of the three-dimensional base and the two-dimensional coating on the block structure are considered. The results of this study complement the articles previously published by the authors with a description of the methods for investigating similar problems in the dynamic mode and interpret the approach for the mechanical evaluation of the stress level of lithospheric plates illustrated at the site (Babeshko Russian National Joint Used Centers for Seismology (Net). EPOS Preparatory Phase Regional Conference; March 19–21, 2012; Prague. http://rp7.ffg.at/eu-russian_opendays). It is shown that, when using the topological method for solving boundary-value problems, consideration of both types of statement of boundary-value problems is reasonable rather than trying to construct the solution of the static problem by the limiting transition from the dynamic problem.