The thesis's subject is about creation and modeling of a solid state hydrogen tank using magnesium hydride (MgH2). The main characteristic of this tank is the ability to store the heat of absorption due to the use of a Phase Change Material (PCM). In order to prove the sustainability of this system, a study, on the magnesium hydride's behavior, has been carried out. On one hand, kinetic properties and the amount of the stored hydrogen do not decrease after 100 cycles. On the other hand, a significant change on material morphology has been noticed. Indeed, a swelling and an increasing of thermal conductivity have been measured. Investigations about the MCP showed the importance of the thermal conductivity and the heat of fusion. That's why a metallic eutectic alloy has been selected. His atomic composition is Mg69Zn28Al3, he is a good thermal conductor, having a high heat of fusion, and presenting a good chemical stability during cycling. The designed tank contains 10 kg of magnesium hydride ball-milled added with Expanded Natural Graphite. It can absorb 7000 NL (625 g) of hydrogen in 3 hours and a half. On one total cycle, the energetic efficiency can be estimated to more than 70 %. At the same time, two numerical modeling have been achieved with Fluent and Matlab softwares, in order to make the design of next generation of tanks easier.