Abstract As the largest population of high mass X-ray binaries, Be/X-ray binaries provide an excellent laboratory to investigate the extreme physics of neutron stars. It is generally accepted that Be stars possess a circumstellar disc, providing an additional source of accretion to the stellar winds present around young hot stars. Interaction between the neutron star and the disc is often the dominant accretion mechanism. A large amount of work has gone into modelling the properties of these circumstellar discs, allowing for the explanation of a number of observable phenomena. In this paper, smoothed particle hydroynamics simulations are performed whilst varying the model parameters (orbital period, eccentricity, the mass ejection rate of the Be star and the viscosity and orientation of the disc). The relationships between the model parameters and the disc’s characteristics (base gas density, the accretion rate of the neutron star and the disc’s size) are presented. The observational evidence for a dependency of the size of the Be star’s circumstellar disc on the orbital period (and semi-major axis) is supported by the simulations.