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This article discusses methods for numerical modeling of geofiltration processes in groundwater, as well as the development and implementation of the proposed methodology for solving hydrogeological problems. The article analyzes the flows of grout waters entering underground aquifers in the form of filtration, and offers optimal solutions for the construction of drainage systems in mountainous areas. The main attention is paid to the development of mathematical models that describe the processes of interaction between groundwater and surface water, taking into account various natural and anthropogenic factors. The article describes methods for predicting changes in the level and state of groundwater, as well as calculating water balance elements. The authors propose mathematical models for describing the movement of groundwater in single-layer media, taking into account the processes of saturation and infiltration. Attention is paid to the use of information technology, mathematical modeling systems and geoinformation technologies to improve the accuracy of hydrogeological research results. The work demonstrates the relevance and prospects of the application of the proposed methods for solving problems of rational use and management of water resources, as well as for the development of new approaches in the field of melioration and water supply. As examples, studies of geofiltration processes in the mountainous regions of the Republic of Uzbekistan are given, where recommendations for the optimal use of groundwater in drinking water supply and irrigation have been developed. [ABSTRACT FROM AUTHOR]