By making use of recently obtained theoretical and Monte Carlo simulation results for solid state thermodynamics and solid-fluid equilibria for systems of hard dumbbells a generalized van der Waals theory of solid-fluid equilibria has been formulated. The theory predicts how the temperature dependence of the solid-liquid (and vapour-liquid) equilibrium is influenced by non-spherical molecular shape for diatomic molecules. Two regimes of behaviour are identified, depending on whether the underlying hard dumbbell reference system freezes into a plastic crystal or an orientationally ordered crystal. The theory correctly predicts a decrease in the triple point temperature and density change on freezing between spherical molecules, such as argon, and slightly non-spherical molecules which freeze into plastic crystal phases such as nitrogen. An extension of the theory which includes a simplified treatment of the influence of quadrupolar interactions provides a plausible explanation for the relatively high reduced triple point temperature of carbon dioxide.