Metal hydride alloys are considered as a promising alternative to conventional hydrogen storage cylinders and mechanical hydrogen compressors. Compared to storing in a classic gas tank, metal hydride alloys can store hydrogen at nearly room pressure and use less volume to store the same amount of hydrogen. However, this hydrogen storage method necessitates an effective way to reject the heat released from the exothermic hydriding reaction. In this paper, a finned conductive insert is adopted to improve the heat transfer in the cylindrical reactor. The fins collect the heat that is volumetrically generated in LaNi₅ metal hydride alloys and deliver it to the channel located in the center, through which a refrigerant flows. A multiple-physics modeling is performed to analyze the transient heat and mass transfer during the hydrogen absorption process. Fin design is made to identify the optimum shape of the finned insert for the best heat rejection. For the shape optimization, use of a predefined transient heat generation function is proposed. Simulations show that there exists an optimal length for the fin geometry.