The objectives of the present study were to perform a numerical analysis of the solidification and melting of water around a vertical heat transfer plate with pin fins by means of a finite-difference method under a quasisteady-state assumption. The characteristics of phase change, such as the shape of the solid-liquid interface, the temperature distribution and the liquid velocity, were considered for different numbers of fins, and these analytical results were compared with the experimental results. We found that the heat conduction underwent a considerable increase when the number of fins was large during the solidification, but in the range near the heat transfer plate natural convection between the fins was confirmed for every number during the melting and small-scale natural convection around the pin fins was defected.