Experiments were performed to study freezing on a finned vertical tube when either conduction in the solid or natural convection in a liquid controls the heat transfer. Conduction is the controlling mode when the liquid is at its fusion temperature, whereas natural convection controls when the liquid temperature is above the fusion value. The liquid was housed in a cylinderical containment vessel whose surface was maintained at a uniform, time-invariment temperature during a data run, and the freezing occurred on a finned vertical tube positioned along the axis of the vessel. The phase change medium was n-octacosan, a paraffin which freezes at about $61^{circ}C$. For conduction-controlled freezing, the enhancement of the frozen mass due to finning is greatest when the frozen layer is thin and decrease as the layer grows thicker. The degree of enhancement is generally less than the surface area ratio of the finned and unfinned tube.