The paper deals with the problem of managing the supplies of consumables (energy resources, lubricants, explosives, explosive supplies, tires, spare parts, etc) in mines. After the introductory remarks and comments, a general stochastic model of supply, relating in general to the dynamic programming method is presented. A selection of stochastic supply model for experiments and research by the authors of this paper is not a coincidence, based on of their long experience, showing that this type of model is the most suitable to provide support for decision-making and management of supplies of consumables in mines.In order for the problemofconsumablessupplymanagement to be reviewed, in whole and objectively from the aspect of risk, experimental tests of the stochastic model in real conditions were performed at the limestone open pit mine Zelenikovec' near Skopje, the capital of Macedonia. The scope of the experimental research enabled reliable analysis. The results obtained confirm the efficiency and reliability of the stochastic model and two separate manipulative-operational positions regarding its application, which may have an important influence on the optimisation of supplies.