This chapter provides semi-analytical solutions for the Stefan problem, which describes the freezing of phase change materials (PCMs) in finned cylindrical storage tanks. These setups use PCMs in the shell and apply boundary conditions at the inner wall to reduce heat loss and speed up phase change. The analysis simplifies the two-dimensional problem into two one-dimensional areas within a symmetric control volume. Region 1 looks at radial heat conduction from the inner wall, while Region 2 considers heat transfer along the fin length. The governing equations are solved using a similarity parameter and the quasi-steady method under constant temperature, constant heat flux, and convective boundary conditions. The chapter determines the position of the freezing front and the temperature distribution for each case. A dimensionless formula for the solid PCM-to-cell volume ratio is developed to estimate total solidification time. A comparison with enthalpy-based numerical results shows that the model is accurate and useful for optimizing thermal storage design.