The reaction between metal hydride (MH) and hydrogen gas generates substantial amount of heat. It must be removed rapidly to sustain the reaction in the metal hydride hydrogen storage reactor. Previous studies indicate that the performance of the reactor can be improved by inserting an efficient heat exchanger design inside the metal hydride bed. In the present study, a cylindrical shaped metal hydride system containing LaNi₅, integrated with a finned tube heat exchanger assembly made of copper pin fins and tubes, is presented. A 3-D numerical model is formulated in COMSOL Multiphysics 4.4 to study the transient behavior of sorption process inside the reactor. Experimental data obtained from the literature is used to approve the legitimacy of the proposed model. Influence of various operating and geometric parameters on the total absorption time of the reactor has been investigated. It is found that hydrogen supply pressure is the most influencing factor to increase the absorption rate of hydrogen. Total absorption time of the reactor is found to be 636 s with maximum storage capacity of 1.4 wt% at the operating conditions of 15 bar H₂ gas supply pressure, heat transfer fluid temperature of 298 K and flow rate of 6.75 l/min.