External and internal flows of pure vapor experiencing film condensation on an appropriately cooled wall are computationally simulated. The stratified/annular flow regimes considered here are such that the vapor flow is either laminar or turbulent while the liquid condensate flow is always laminar. For negligible droplet entrainment into the vapor phase, both smooth and wavy interface situations are considered. A full two dimensional numerical solution strategy is presented. This strategy is then implemented for smooth interface laminar/laminar flows. The simulations for the classical problem of film condensation on a tilted (horizontal to vertical) plate are in very good agreement with established classical solutions. For wavy interface turbulent/laminar flows, only a one dimensional approach is implemented. This approach employs suitable semi-empirical interfacial shear models for wavy flows which yield predictions in reasonable agreement with experiments.