The hydrogen storage system LiH + NH(3) ↔ LiNH(2) + H(2) is one of the most promising hydrogen storage systems, where the reaction yield can be increased by replacing Li in LiH with other alkali metals (Na or K) in order of Li < Na < K. In this paper, we have studied the alkali metal M (M = Li, Na, K) dependence of the reactivity of MH with NH(3) by calculating the potential barrier of the H(2) desorption process from the reaction of an M(2)H(2) cluster with an NH(3) molecule based on the ab initio structure optimization method. We have shown that the height of the potential barrier becomes lower in order of Li, Na, and K, where the difference of the potential barrier in Li and Na is relatively smaller than that in Na and K, and this tendency is consistent with the recent experimental results. We have also shown that the H-H distance of the H(2) dimer at the transition state takes larger distance and the change of the potential energy around the transition state becomes softer in order of Li, Na, and K. There are almost no M dependence in the charge of the H atom in NH(3) before the reaction, while that of the H atom in M(2)H(2) takes larger negative value in order of Li, Na, and K. We have also performed molecular dynamics simulations on the M(2)H(2)-NH(3) system and succeeded to reproduce the H(2) desorption from the reaction of Na(2)H(2) with NH(3).