The vapour - liquid equilibrium of short n-alkanes is considered by using perturbation theory. This requires as a previous step obtaining an equation of state (EOS) for hard flexible models. An EOS for hard-n-alkane models which shows excellent agreement with computer simulation of hard-n-alkane models with up to 100 carbon atoms is proposed. This EOS is combined with a mean-field term and the vapour - liquid equilibrium of n-alkanes is computed. When theoretical critical densities and pressures are plotted as a function of the number of carbon atoms, a maximum is found. This is in agreement with experiment. The conditions for the appearance of such a maximum in general chain models are established. Some ways of improving the mean-field theory are suggested.