Mesoporous polysaccharide aerogels are versatile functional materials for drug delivery and wound dressing devices. The hydration and wetting of these aerogels control their application-related performance, e.g. the release of encapsulated drugs. Reported here is a detailed small-angle neutron scattering (SANS) analysis of the hydration mechanism of a calcium alginate aerogel, based on mathematical modelling of the scattering. The model accounts for the hierarchical structure of the material comprising a mesoporous structure, the solid skeleton of which is made up of water-swollen polymers. At large scale, the mesoporous structure is modelled as a random collection of elongated cylinders, which grow in size as they absorb water and aggregate. The small-scale inner structure of the skeleton is described as a Boolean model of polymer coils, which captures the progressive transition from a dense dry polymer to a fully hydrated gel. Using known physico-chemical characteristics of the alginate, the SANS data are fitted using the size of the cylinders as the only adjustable parameter. The alginate aerogel maintains a nanometre-scale, albeit altered, structure for low water contents but it collapses into micrometre-sized structures when the water content approaches one gram of water per gram of alginate. In addition to the wetting of aerogels, the model might be useful for the small-angle scattering analysis of the supercritical drying of gels.