The moving heat source model and the Green's function method were applied to solve for the phase change problems involved in the freezing and thawing processes of biological skins with finite thickness. The transient temperature distributions, the cooling and warming rates, etc. inside the skin subject to two typical boundary conditions (the convective or plate cooling) often encountered in skin cryo-preservation are analytically predicted. And the heat transfer performances of these two freezing (or thawing) approaches are comparatively discussed. Implications of the present closed form analytical solution to the other biological phase change problems such as the skin cryosurgery or rewarming by microwave were also suggested.