The invention relates to a compacted material containing magnesium hydride and expanded natural graphite and to a method for preparing one such material including the following steps in which: (i) a powdered magnesium or magnesium hydride is mixed with a powdered graphite, and (ii) the mixture is shaped by means of compaction. The invention also relates to the use of said material for the storage of hydrogen as well as to a method for hydrogen storage and release from storage, including the following steps in which: (a) the aforementioned material is placed in a suitable hydrogen tank, (b) the material is placed under hydrogen pressure in pressure and temperature conditions that enable the hydrogen to be absorbed by the material, and (c) the hydrogen is desorbed from the material in pressure and temperature conditions that enable the desorption of the material.