Research objective is to identify the features of stress-strained state development and estimate the stability of Unglichikan open pit walls and dump slopes based on calculation, analysis, and estimation with the certified finite element method GenIDE32. The introduction describes features of research object location natural-technogenic conditions and geological history of rocks building up the research object. Research relevance is due to complex solution to deep and high mountain structures design problems, account for construction technologies, and stress-strained state and elements stability determination. Methods of the stress-strained state numerical calculation, analysis, and estimation for the “structure– geological environment” system consists in using all tools of the program’s interface, namely, values, value levels, isolines and graphs for different quantities, including the graphs of stress-strained state behavior trajectories in the space of the stress tensor invariants and relative strains. Results of calculation are presented as the program’s capabilities in graphic representation of the sequential development of mudslides in open pit walls and dump slopes with vertical fissures. Colors of magnitude levels specify the contours of mudslides, while the corresponding shading of finite elements indicates the fissure formation sites. Conclusions. Calculation results proved the stability of the mountain structures for the selected size dimensions of open pit walls and dump slopes.