In this study, an analytical approach is used to find expressions for the closure time in freezing processes for spheres and cylindrical tubes. The starting point is the well-known two-phase Stefan problem. A new characteristic solution is established for extending the theory of constant heat flux ratio. Next, temperature profiles are assumed and substituted into the interface equation, which are then solved for the inward freezing process to get the closure time. Plots are generated to compare the new expressions to previously published experimental results of closure time. The new analytical approximations give reasonable outcomes as discussed in this paper. This paper demonstrates a general approach that can be further applied to different types of phase-change problems.