The presented work deals with the improvement of the evaporation model of the ATHLET (Analysis of Thermal and Hydraulics of Leaks and Transients) system code to be applied to a passive containment cooling system of a nuclear power plant. For the model validation, INTRAVIT (Investigation of Passive Heat Transfer in a Variably Inclined Tube) test facility setup at the University of Luxembourg was used. The first part of the paper presents a review of the existing literature on evaporation models that revealed that those models significantly simplify the physical processes that occur. Next, a modified evaporation model is proposed that offers a realistic description of various evaporation processes and the start of bubble formation using a nucleation model, and a surface density calculation model is introduced that is necessary for evaporation simulation. The final part of this work explored five different system configurations to test the evaporation model: three condenser tube inclinations (5 deg, 60 deg, and 90 deg), two riser lengths (1 m and 2.5 m), and different thermal loads. They made it possible to simulate several experiments for stable and unstable natural circulation and to verify the proposed model.