The operation of the SF6 puffer circuit breaker relies on he pressurisation of gas by a combination of piston compression, nozzle blocking and gas heating. Theoretical modelling of the physical processes occurring during high-current interruption is important for mechanical design and for prediction of electrical performance. A high-current arc model has been developed, which takes account of observed gas behaviour throughout the arcing period and beyond current zero. The predicted pressurisation is compared with experimental work, and shows good agreement over a wide range of operating conditions. The theoretical model pays particular attention to the mechanisms of heat transfer within the upstream region of the interrupter, and incorporates a new description of the arc thermal boundary.