There is a possibility that hydrogen absorbing alloys will generate unexpected stress in an alloy bed and deform or destroy the vessel because the alloys expand when they absorb hydrogen. The amount of stress generated on the vessel surface by alloy swelling was measured with the object of elongating the life time of the reaction vessel in heat utilization systems that use hydrogen absorbing alloys. As a result, it was found that 1) localized stress is generated at the bottom of the vessel due to hydrogen ab-/desorption cycles with an alloy packing fraction of 50 vol %, and this stress not only increases with each cycle, but also continues to increase even after plastic deformation of the vessel, 2) stress accumulation depends on the amount of hydrogen ab-/desorption and on the initial packing fraction, and 3) the mechanism for stress accumulation can be estimated as a two-step process in which agglomeration between the hydride particles occurs when the packing fraction of hydride is higher than 61 vol % in the initial cycles (Step 1), and then fine powder generated by pulverization during the cycles falls in gaps at the bottom of the vessel and causes the hydride packing fraction at the bottom of the vessel to gradually increase (Step 2).