The phenomenon of one‐dimensional steady condensation of pure vapor at the plane surface of a liquid is considered from the kinetic theory viewpoint. The vapor is treated as a perfect gas without internal degrees of freedom. For the description of this problem the full nonlinear BGK model equation is used. For the solution of the BGK model equation the method of discrete ordinates is applied. The calculations are carried out for water vapor. As a result the temperature and density distributions in the vapor phase are obtained and also for a given temperature difference the net condensation molecular flux rate is determined, depending on the condensation and evaporation coefficients which are treated as parameters.