The paper contains analytical overview of the most important unique/critical objects and the computational analysis problems of the mechanical safety, carried out by the team of Research & Development Centre StaDyO (StaDyO R&D Centre) researchers for the last two years (2016-2018). Corresponding complex coupled problems of continuum mechanics were solved with the use of contemporary methods and models of numerical modeling (nonlinear models, coupled problems, substructures, submodeling, etc.), implemented in verified software complexes. Some of these results are briefly considered and analyzed. Conclusions about the main directions of further research and development are presented as well. © Published under licence by IOP Publishing Ltd.