The shielding analysis of the spent fuel dry storage cask TN-32 is carried out using the continuous-energy Monte Carlo neutron- and photon-transport code MCS developed by the Computational Reactor Physics and Experiment laboratory of the Ulsan National Institute of Science and Technology. The shielding analysis involves the transport simulation of the decay neutrons and gammas emitted by the spent fuel to obtain the neutron and gamma dose rate values outside of the cask. This deep-penetration problem is solved by means of weight window population control as variance reduction. The TN-32 cask calculations are repeated with the MCNP6 Monte Carlo code for verification purpose and a good agreement within three standard deviations is observed between MCS and MCNP6. The neutron dose rate on the cask surface and 2 m away from the cask can be calculated with MCS, whereas the photon dose rate calculation for positions outside of the cask will be further improved by employing more sophisticated variance reduction techniques.