Cancer treatment with proton therapy, starting in 1946, continues with the treatment of 200,000 patients worldwide as of 2020. The energy release of protons in tissue and tissue equivalent (water) material is shown by Bragg Curves. The main reason why proton beams are preferred in radiotherapy is that the proton beams continue on their way by giving maximum energy to the tissue to be treated and giving the least damage to the healthy tissue. In this study, with the help of Monte Carlo-based GEANT4 and TRIM simulation programs, Bragg peak positions in the 60 – 130 MeV energy range are given for water and brain by using the relativistic Bethe – Bloch equation. The difference between GEANT4 and TRIM was 7.4 % on average in the water phantom, while the difference was 7.6 % in the brain phantom. Bragg peak position was calculated for water and brain phantoms at 0.6, 0.8 and 1.0 cm thicknesses, which is suitable for the average thickness of the cortical bone in the skull. An average of 8.1 and 7.8 % deviations were detected between the two simulation systems in the cortical bony, water and brain phantoms with three different thicknesses. The values found were compared with the clinical studies available in the literature.