In Korea, an advanced reactor system of 330MWt power called SMART (System integrated Modular Advanced ReacTor) is being developed by KAERI to supply energy for seawater desalination as well as electricity generation. A shielding design of the SMART core with 49 CEDM is established by a two-dimensional discrete ordinates radiation transport analyses. The DORT two-dimensional discrete ordinates transport code is used to evaluate the SMART shielding designs. Three axial regions represent the SMART reactor assembly, each of which is modeled in the R-Z geometry. The BUGLE-96 library is used in the analyses, which consists of 47 neutron and 20 gamma energy groups. The results indicate that the maximum neutron fluence at the bottom of reactor vessel is $5.89 { imes} 10^{17};n/cm^2$ and that on the radial surface of reactor vessel is $4.49 { imes} 10^[16};n/cm^2$. These results meet the requirement, $1.0 { imes} 10^{20};n/cm^2$, in 10 CFR 50.61 and the integrity of SMART reactor vessel during the lifetime of the reactor is confirmed.