Reliable design, analysis and optimization of on-board adsorptive hydrogen storage systems require mathematical models that capture the key physics across multiple scales. Pellets of adsorbent may sometimes be preferred for adsorptive storage in fixed beds, compared to powders. Heat and mass transfer within individual pellets play a significant role in the overall dynamics of a fixed bed filled with adsorbent pellets. However, multiscale dynamical model that captures the effect of pellet behavior on the overall dynamics of adsorbent bed is so far missing. In this study, a combined bed–and–pellet “1D-plus-1D” model is developed and analyzed for hydrogen adsorption in a fixed bed of MOF-5 pellets at cryogenic temperatures. Specifically, a 1D axial bed model with mass, momentum and energy balance equations is coupled with a 1D radial pellet model comprising of mass and heat transfer with adsorption within the pellets present at different locations in the bed. The 1D bed and 1D pellet model equations are coupled through surface fluxes on the pellet. We show that internal diffusional resistances within pellets must be considered for pellets greater than 2 mm diameter, for parameters relevant to MOF-5 pellets. The role of various physical parameters of pellets is analyzed.