A two-dimensional mathematical model to predict the thermal performance of an adiabatic hydrogen storage system based on the combination of magnesium hydride and magnesium hydroxide materials has been developed. A simple geometry consisting of two coaxial cylinders filled with the hydrogen and thermochemical heat storage materials was considered. The main objective was to gain a better knowledge on the thermal interaction between the two storage media, and to determine the dependence of the hydrogen absorption time on the geometric characteristics of the reactor as well as the operation conditions and the thermophysical properties of the selected materials. The dimensions of the two compartments where the two materials are filled were chosen based on the results of a preliminary analytical study in order to compare the absorption times obtained analytically and numerically. The numerical results have shown that the hydrogen absorption process can be completed in a shorter interval of time than analytically as a result of the larger temperature gradient between the magnesium hydride and magnesium hydroxide beds. This was mainly due to variation of temperature in the thermochemical heat storage material during the more realistic dehydration reaction in the numerical solution. Larger temperature gradients, thus a faster hydrogen absorption process can also be achieved by increasing the hydrogen absorption pressure. Moreover, it was found that the increase of the thermal conductivity of the magnesium hydroxide material is crucial for a further improvement of the performance of the MgH2-Mg(OH)2 combination reactor.