Adsorption phenomena are encountered in several engineering applications. One of its uses is in the storage and transport of gas in the form of adsorption tanks. The exothermic nature of the adsorption process decreases adsorption capacity presenting an impetus to understand the thermal characteristics of the gas storage process. Studies using mixtures of phase change materials and adsorbents in adsorption tanks demonstrate potential improvements in the adsorption capacity of the tanks. They also show that the distribution of phase change materials and adsorbent are important. Thus, this work presents two approaches for optimising the adsorbent domain. The first is to use a semi-analytic model to determine the best homogeneous material concentration for the adsorbent and phase change material for the vessel composition. The other is to use a 2D axisymmetric model to perform FGM optimisation to distribute material in the tank. Results for both models are presented and discussed for different conditions. The study shows that, for the cylindrical geometry, FGM optimisation is always, at least, marginally better than the homogeneous distribution from the semi-analytic model. However, FGM optimisation demands more computing time increases the complexity of implementation and results assembling. The semi-analytic approach is a possible alternative for optimising adsorption systems with phase change material mixed with adsorbents.