Deposition of elemental sulphur in natural gas transmission line systems has been reported on only in recent times. The most common location is immediately downstream of a point of significant pressure reduction. A necessary step to eliminate solid sulphur deposition is to understand the deposit mechanism. Two mechanisms appear possible: condensate formation and desublimation of sulphur vapours. To study the plausible paths of solid sulphur formation, we established a thermodynamic model. The constitutive equations are classically the chemical and physical equilibriums, partial mass balances and energy balance. We chose the Peng Robinson equation of state to describe the phase behaviour. Mixing rules are conventional: quadratic for a and linear for b with one binary interaction coefficient. Desublimation seems to be the most plausible mechanism to explain the solid sulphur formation. Pressure reduction implies temperature reduction, which reinforces solid formation. A solution to minimize the solid sulphur deposition seems to be heating the gas stream immediately before pressure reduction.