The stability of the stoichiometric solid structures Xe(He)2 and Xe(He)13 is investigated up to 30 GPa pressure at room temperature, T=300 K. The Gibbs free energy of these so-called van der Waals compounds is computed using simple semianalytical methods that are in good agreement with molecular dynamics computer simulations. The interatomic interactions are described by empirical pair potentials adjusted to fit high pressure experimental data. The Xe(He)2 phase is found to be stable with respect to phase separation into pure components, while Xe(He)13 is unstable. These results agree with simple packing considerations, but are rather sensitive to the precise form of the helium–xenon interaction. A brief comment is made about the occurrence of a Ne(He)2 compound, that was recently found by Jean-Louis et al.