Composite materials consisting of a salt-impregnated porous host matrix constitute a way to combine the high energy storage density of hygroscopic salts with the fast kinetics of the carrier material. Depending on its pore structure the carrier can furthermore prevent or inhibit leakage of the salt solution. It has been shown experimentally that by impregnation with CaCl₂ the heat storage density of zeolite Ca-X can be increased by 53 % to 270 kWh m⁻³, which confirms the potential of this material class. In transforming this potential into technical heat storage solutions, numerical simulations can support the design process by bridging the gap between material characterization, process specification and reactor design. Such simulations rest, among others, on suitable constitutive relations. For the equilibria and kinetics of salt/zeolite composite sorbents those relations are still missing in the literature. In this work, we present an axisymmetric model of the mass and heat transport through a packed bed of composite sorbent pellets accounting for radial effects such as increased bed void fraction near the sorption chamber walls. Special focus is laid on the modelling of the sorption equilibria and kinetics of CaCl₂/zeolite Ca-X composites of various salt loadings. The developed sorption equilibrium model for arbitrary salt loadings of the CaCl₂/zeolite Ca-X is based on isotherm measurements of only one composite sample and one sample of pure zeolite Ca-X thereby enabling reduced experimental effort for the equilibrium characterization. The linear driving force kinetics is calibrated using data from dynamic sorption experiments on zeolite Ca-X and used to predict the dynamic sorption behaviour of CaCl₂/zeolite Ca-X composites. We found a good predictive capability of the unmodified kinetics model for high inlet humidities—i.e., the practically most relevant cases where the composite plays its strengths. Contrarily, for low inlet humidities, the used kinetics model strongly overestimates the sorption rate, which indicates the presence of additional kinetic inhibition mechanisms under such conditions.