Many modelling studies have been conducted on single metal-hydride (MH) beds subject to, for example, a sudden increase in hydrogen pressure. In a practical MH thermodynamic machine such as a hydrogen compressor or heat pump, however, one bed is heated and desorbs into a second, cooled bed. This two-part study presents a two-dimensional axisymmetric mathematical model for such thermodynamic machines, simulating two interconnected cylindrical MH tanks, constrained so that the mass flow rate from the desorbing bed equals the inlet flow rate of the absorbing bed. Part 1 covers the development of the model and its validation against experiment. Key practical MH characteristics like expansion, hysteresis and plateau slope are accounted for. Implemented using COMSOL Multiphysics, the model simulates horizontal annular reactors containing different AB5 alloys, with finned coaxial heat exchangers. This configuration was chosen to expose the existence and consequences of internal temperature gradients arising in the low effective thermal conductivity of MH beds. The model incorporates mathematical formulations to account for variations in bed porosity and permeability arising from changes in alloy particle diameter during volumetric expansion and contraction induced by hydrogen absorption and desorption. These variations influence the effective thermal conductivity within the bed, which is also captured by the model. In Part 2 the model is utilised to investigate the underlying physics governing coupled-reactor operation, with its advantages over conventional single-reactor models comprehensively analysed.