We describe a study of the phase diagram of a nonlinear triatomic molecule with hard sphere interactions between the sites using isobaric ensemble Monte Carlo simulations. The model is constructed so as to serve as a hard sphere interaction site model of propane. Several different crystal structures were used to initialize the solid phase simulations. An apparently optimum crystal geometry was located by allowing the Monte Carlo simulation cell shape to fluctuate. The fluid phase was found to be stable over a range of volume fractions, which is 35% greater than for a system of hard spheres with the same molecular volume. The fractional density change on freezing is about 4%. When the free energy for the model is used in a generalized van der Waals theory of solid-fluid equilibrium it predicts low values of the triple point temperature and fractional density change on freezing which are qualitatively similar to those for propane.