Artificial ground freezing has been applied to many geotechnical projects as temporary and permanent ground stabilization. This paper presents numerical formulations implemented in SMAP-T2, which is specially designed for geotechnical applications of heat transfer problems, along with a new efficient method to compute average heat capacity at freezing point. As one of the practical applications, a frozen backfilled egress shaft is presented in this paper. The aim of this example is to evaluate time requirements for freezing and maintaining the frozen shaft, to evaluate freezing front migrations and possible insulation schemes, and to assess the relative advantages of various stemming materials such as pure water and combinations of soil/water mixtures.