Based on an analysis using the Carnahan–Muller shape factor approach, mathematically simple and physically sound equations of state for fluids of non-spherical hard particles are proposed. The analysis has been performed using two versions of the statistical associating fluid theory for chains of hard-spheres, the hard convex body equation of state of Boublik and Nezbeda (Collect. Czech. Chem. Commun., 1986, 51, 2301) and the Flory-dimer model of Honnell and Hall (J. Chem. Phys., 1989, 90, 1841). The combination of the shape factor concept with the recently developed generalized biquadratic equation of state BQ75 gives access to simple biquadratic equations of state for different molecular shapes. With the combination of these two methods it is possible to simplify macroscopic models for molecular fluids. Furthermore the generalized method proposed here can be used to obtain simple equations of state from data generated by molecular simulations.