The dry storage cask became a semi-permanent solution for spent nuclear fuel since no permanent solution has been finalized over the past three decades. Considering the difficulty of deep geological repository projects in many aspects, prolonging the service life of dry casks longer than a few decades has become an option for spent nuclear fuel storage. It must be ensured that dry cask safety objectives, including radiation shielding, criticality safety, structure health, decay heat removal, and containment be fulfilled during the prolonged service life. This paper presents numerical modeling results of the radiation dose rate distribution on a TN-32 cask surface aged up to 300 years. The numerical modeling method was validated with measurement data, and the difference between the calculated results and measurement data in the total dose rate is 7%. The detailed radiation distribution variations over cask surfaces along the axial and radial directions for 300 years of storage were obtained, and their azimuthal angular dependence was established. The maximum total dose rate over the cask surfaces is less than 10 mrem/hour (9.258 ± 0.212 mrem/hour) after 40 years, and this outcome fulfills all dose rate requirements from 10 CFR 71.47(b). After 300 years of storage, the average total dose rates on the side surface and top surface are 0.150 ± 0.007mremmrem/hour and 0.057 ± 0.003mremmrem/hour, respectively, while the maxima are 0.601 ± 0.014 mrem/hour and 0.112 ± 0.006 mrem/hour, respectively. The variations in the fuel gamma ray, structure gamma ray, neutron and secondary gamma-ray contributions to the total dose rate are presented and analyzed in this work. The neutron and gamma-ray dose rate contributions by energy group are presented and analyzed at the cask top, mid-plane, and bottom at the selected storage times.