The aim of this work is to develop and evaluate a mathematical model for the process of storing hydrogen obtained from hydroelectricity via electrolysis, for use as an energetic vector in rural areas of Venezuela. Following an exhaustive bibliographical review of the subject, pressurized containers were chosen as the most appropriate means of storage. The components of the compressed H2 gas storage systems to be modelled are 1) the Compression Unit, CU, and 2) the Storage Unit, SU. With this information and by using non-linear regression methods, we developed a mathematical model with which to study the behaviour of the main variables involved in the storage process: the quantity of H2 to be stored, the storage pressure, energy consumption, the size of the compressor, and the unit cost of the containers. In structural terms, the mathematical model comprises an energy model and a financial model. The results show that there is a range of operating conditions with a minimal overall cost, as a result of the behaviour of the investment cost, which define how the total costs evolve.