The NA62 experiment is a fixed target experiment located in the North Area of CERN and has as main goal the measure- ment of the branching ratio of the rare decay 𝐾+ → 𝜋+𝜈𝜈. The primary proton beam from the SPS accelerator interacts with the T10 beryllium target and the generated 75 GeV/c secondary particles, containing about 6% of positive kaons, are transported by the K12 beamline to the NA62 experi- ment. Studies in this paper present detailed simulations of the K12 beamline developed in both FLUKA and BDSIM codes, which reproduce the current configuration of K12 for the NA62 experiment. The beam optics parameters of K12 are studied in BDSIM and compared to MADX optics and tracking calculations. The models in FLUKA and BD- SIM are used for beam studies at various locations along the beamline, and the parameters obtained from simulations are benchmarked against data recorded by the experiment. The impact of the Cherenkov kaon tagging detector (CEDAR) on the beam quality is calculated for two different gas com- positions in view of a possible upgrade of the detector.