Condensation of vapours on a vertical fin in the presence of non-condensable gas is formulated and solved for a wide range of system parameters, making use of the analogy between heat and mass transfer. The formulation enables the derivation of special cases such as condensation of vapours on a vertical isothermal surface with and without non-condensable gas in the vapour. Besides, the analysis of condensation of vapour on a fin has revealed non-isothermal conditions of the thin fin with the temperature of the liquid-vapour interface also changing along the length of the fin. The numerical results from the analysis are rendered into dimensionless equations that can be used to predict the mean condensation heat transfer coefficients.