The evolution of stratified liquid natural gas (LNG), from its formation to its breakdown, is considered. Experimental observations have shown this evolution to consist of two principle phases : a quiescent, stable phase 1 where the interface between the two layers is stationary; and an unstable phase 2 characterised by a migrating interface and culminating in a rollover. Mathematical models of the two phases are proposed and considered separately. For phase 1 a parametric solution is derived; the corresponding numerical solution of phase 2 equations is given and shown to compare well with experimental data.