This paper presents several steady-state neutron transport models which are used to determine the behaviour of the nuclear criticality incident that occurred at the Windscale Works in 1970. The transfer vessel involved in this incident contained two immiscible fissile liquids (an aqueous phase and an organic phase) which had been disturbed such that an emulsion layer formed between them. Infinite domains of the aqueous, organic, and emulsion phases were modelled to enable the understanding of the effects of nuclear data library, neutron transport code and material on the calculated kinetics data, effective multiplication factor and macroscopic neutron cross sections. Six possible configurations of the 1970 Windscale criticality incident were simulated using three-dimensional models in MCNP, two-dimensional models in academic research code EVENT, and one-dimensional models in a collision probability (CP) code. Quantities of interest, such as reactivity, scalar neutron flux, neutron absorption and production rates, and kinetics data are presented. System reactivity, mean neutron generation time and neutron absorption and production rates are shown to increase with increasing emulsion thickness, whereas the total scalar neutron flux is shown to decrease. It is determined that the volume of organic phase present during the transient was likely to be around 39.0 L, as the emulsion thickness required to reach criticality (6.5 cm) was within the range cited in the literature. EVENT and the CP code showed deficiencies when calculating the scalar neutron flux through the plenum gas at the top of the transfer vessel, with the CP code overestimating the total scalar neutron flux in the system by as much as 19 %. The intrinsic neutron source, subcritical multiplication and subcritical power of the system were computed using Monte Carlo simulations. It was shown, by use of the Hansen criteria, that the subcritical system was likely to be in a strong neutron source regime (such that stochastic variations in neutron population are negligible when regarding nuclear criticality transients). In addition, it was computed that a vessel containing 39.0 L of organic solvent had a subcritical power of 10.81