This paper puts forward a mathematical model of transport processes in a metal hydride packed bed along with an analytical quantification of the frequently used assumptions. The complete model takes into account heat transfer by conduction, convection, mass transfer, as well as reaction kinetics and convective interactions between the fluid and solid phases. By analyzing several frequently used assumptions, a system of useful and practical analytical criteria is obtained. The criteria reveal when simplifications of the model are possible. The sampled models obtained by reduction of the complete model can be effectively used in describing transport processes in metal hydride beds within the limits determined by a set of analytical criteria. Specifically, criteria for the validity of local thermal equilibrium, steady-slate approximation, the frontal model approximation, and the filtration approximation are established analytically.