Problem Statement (Relevance). The paper considers the dependence between stability and efficiency of exploitation of deep pits and a relevant selection of mining technology and facilities. When the pit becomes deeper, minerals transportation conditions are characterized as more complicated, entailing a longer conveying distance, greater rock mass hoisting height and lower performance of production equipment. The paper analyzes the existing designs of hoists and inclined conveyors. It contains a logical rationale for applying the classic brachistochrone problem to simplify a description of conveyance movement. The paper shows one of promising solutions to improve open pit transport with conveyances, moving along guidance rails. The descending route is approximated to the brachistochrone, namely a curve of fastest descent. The authors of the paper present the analytical dependence to determine main characteristics of the conveyance descending in open pit mining. The data are used to design a mathematical model of the descending route, as they prove an optimum profile of the route for conveyances. Objective: To show advantages of applying the brachistochrone in conveyance descending to deliver auxiliary materials to zones of open pit mining. Methods Applied. The applied integrated approach is used to solve the issues. Its application in the research implies functioning of scientific analysis methods, compiling data from the published studies, analytical dependence and a system analysis. Practical Relevance. This approach may be used to offset a negative effect of an increased depth of mining on economic performance of the mining plant, when operating deep pits. Mining and conveyor systems of pits are modernized and revamped by introducing promising means of delivery of auxiliary materials adapted to the maximum to the existing infrastructure in the pit.