Monte Carlo computations are reported for LiCl, LiI, NaCl, KBr, KF, KI, RbCl and CsF in both the molten and crystalline phases at T=Tf. With the exception of LiI, KF and CsF the Born–Huggins–Mayer potentials with the Tosi–Fumi parameters reproduce the experimental internal energies very well and the densities fairly well. The model of crystalline LiI at Tf is unstable with respect to fusion at the experimental density. Approximate estimates of polarisation energies in three alkali metal chlorides indicate that these contribute 2–5 % to the potential energy. Radial distribution functions are reported and discussed in comparison with experiment.