Purpose. To develop a mathematical model for a system of amber extraction based upon physical cumulation and deflation effects under the conditions of turbulent flows. Methodology. Theoretical simulation of the extraction processes took into consideration use of a basic aggregate, converting processes, compounding processes, modification processes, aggregating processes, processes of rotation series development involving practices of design and operation of the available similar facilities, design solutions, and widespread unification of both components and assembly units. Analysis of the gained theoretical and practical experiences helped simulate processes of amber extraction from sandy and clay rocks with stope filling. Findings. Rock mass loosening by means of hydromonitor jets, operating tangentially in a casing while developing swirling pulp flows, has been simulated mathematically. A procedure to prepare filling material from mine tailing by means of a preparator, located within a settling pond, has been substantiated. The research, concerning mineral disintegration, has helped identify that the average value of the maximum deflector radius, shaped as a result of counter jetting action, is Rmax = 0.30.5 m; at the same time, the average value of the maximum radius of a hole, shaped resulting from helical jetting action around suction pipe, is Rmax = 0.3m. Originality. For the first time, a mathematical model to use cumulation and deflation effects for a mineral disintegration has been developed as well as for preparation of filling material from mine tailing. The model reflects twists of helical 6585 jetting action with the maximum 0.5 m deflector radius and development of turbulence improving stope filling efficiency. Practical value. The proposed procedure is the theoretical background to develop automated system of amber extraction from sandy and clay rocks, which will improve productive capacity of the mining process substantially.