This work presents the development and implementation of the one-dimensional freezing model in system analysis code SAM (System Analysis Module), code verification using analytical solutions, and code demonstration of a postulated overcooling transient for a fluoride salt–cooled high-temperature reactor (FHR) system and safety analysis applications. This paper first summarizes the freezing model, finite element numerical method, and special numerical treatment for handling transitions between single- and two-phase conditions. Analytical solutions are derived for two cases, with and without solid walls, for code verification purposes. As expected, the numerical results predicted by SAM agree very well with the analytical solution. A code demonstration is then performed on a postulated protected overcooling transient event of a generic reference pebble bed FHR design. The code was found to successfully predict salt freezing during such a postulated event. However, due to the lack of salt freezing testing data, code validation is not performed in this work, but will be pursued in future studies when such data become available.