The completeness indicator is associated with the degree of the natural potential mani- festation and the reliable functioning of geosystems at a constantly high level. This is necessary to ensure sustainable development and effective solutions to environmental management problems. Geography and cartography can solve them using the methods of geoinformation modeling. By the example of the Slyudyansky district’s forests (Irkutsk oblast), the process of realizing the stocks completeness of the geosystem function, their reproduction under different environmental conditions is statistically studied using inventory databases. The mathematical model describes the options for the change in completeness over time, including sustainable growth and development of natural systems. A feature of the model is the existence of a bifurcation point of trends in the completeness of geosystem functions implementation. Sustainable development becomes possible only when the normative performance indicators are overflowed. According to the graphs of the time dependence of changes in forest stocks under various conditions, an assessment was made of the possibility of implementing sustainable management. To differentiate the territory according to the prerequisites for stable development, the methods of landscape-appraisal mapping were used. Geoinformation mapping of geosystem functions was carried out with the allocation of terrain areas recommended for effective nature management according to the criterion of functioning completeness.