This chapter presents semi-analytical solutions for the Stefan problem, which describes the freezing of phase change materials (PCMs) in finned rectangular storage units. Since an exact two-dimensional solution is not feasible, the system is simplified into two one-dimensional regions within a symmetric control volume. In Region 1, heat transfer happens by conduction in the x-direction. This is modeled using the one-dimensional Stefan equation under constant temperature, constant heat flux, and convective boundary conditions. The quasi-steady method and separation of variables are used to find temperature profiles and the motion of the freezing front. In Region 2, heat transfer along the fins in the y-direction is examined using a dimensionless formulation that is solved through Fourier transform techniques. Model predictions are compared with a complete enthalpy-based numerical solution. The results show strong agreement for temperature distribution and interface position. A geometric parameter that represents the solid PCM-to-cell volume ratio is introduced to estimate total solidification time. This helps guide the optimization of thermal storage systems.