The canonical ensemble Monte Carlo technique is used to calculate thermodynamic properties and density distributions of Xe atoms trapped in the alpha cage of zeolite NaA, which is modelled as discrete atoms (or ions) positioned on a truncated cuboctahedron. The addition of Xe atoms to the cage causes a decrease in the calculated potential energy up to a preferred loading. Beyond this, though, further loading becomes energetically unfavourable. The angle averaged density distribution of Xe in the cage exhibits a maximum between the centre of the cage and the wall; both the position and the intensity of this maximum depend strongly on the loading. Detailed examination reveals that localized density maxima exist at discrete points within the cage and that these points move as Xe loading changes. Both the preferred Xe loading and the shape of the Xe density distribution depend strongly on the Si/Al ratio, since this parameter determines the number of charge balancing cations present. For high Si/Al ratios, the angle averaged Xe density distribution can display multiple peaks. The accuracy of the Monte Carlo simulation is demonstrated by comparing the resulting potential energy and density distribution with the numerically integrated solution for the case of one Xe per cage. The numerically computed heat of adsorption for single particle loading compares favourably with experimental values following parameter scaling. The relation of these results with both previously published Xe NMR measurements and with the mobility of adsorbates in zeolites are also explored.