In this paper, a three-dimensional hydrogen desorption model is developed to precisely study the hydrogen desorption kinetics and resultant heat and mass transport phenomena in metal hydride hydrogen storage vessels. The metal hydride hydrogen desorption model, i.e. governed by the conservation of mass, momentum, and thermal energy is first experimentally validated against the temperature evolution data measured on a cylindrical $LaNi_5$ metal hydride vessel. The equilibrium pressure used for hydrogen desorption simulations is derived as a function of H/M atomic ratio and temperature based on the experimental data in the literature. The numerical simulation results agree well with experimental data and the 3D desorption model successfully captures key experimental trends during hydrogen desorption process. Both the simulation and experiment display an initial sharp decrease in the temperature mainly caused by relatively slow heat supply rate from the vessel external wall. On the other hand, the effect of heat supply becomes influential at the latter stages, leading to smooth increase in the vessel temperature in both simulation and experiment. This numerical study provides the fundamental understanding of detailed heat and mass transfer phenomena during hydrogen desorption process and further indicates that efficient design of storage vessel and heating system is critical to achieve fast hydrogen discharging performance.