This paper starts a large research aiming to build up econometric models applicable in mining industry that may be useful for managers working in this economic activities. Being the first one, this article deals mainly with building a dynamic model for resource utilization in mining industry. In his first part, the paper assesses sustainability and the thermodynamic constraints on optimal mining ores depletion in this respect. Starting from these findings, in the second part, a dynamic model of change and substitution techniques for resource utilization in mining industry has been developed. This model will be a useful tool for decision makers for an optimal management in mining industry.