In the case of moist air, moisture condensation takes place when the surface temperature is below the dew point temperature. This is a very common phenomenon in extended surfaces of heat exchangers used in cooling and heat recovery systems. There exist different types of methods in the literature where simultaneous convection and mass transfer have been considered and the results are confusing. In the paper, analytical solutions are presented for straight rectangular and uniform annular fins for the case where that part of a fin the temperature of which is below the dew point temperature is wet and the rest is dry. Also fin efficiencies are derived and shown for typical fins in practical applications. In analytical solutions the convective heat transfer coefficient is assumed known.