This report is an investigation into the melting of axi-symmetric and two-dimensional bogies at a Mach No. of M[infinity] = 1.78 and stagnation temperatures up to 550 [degrees]K. In this temperature range, the most suitable material for the models was found to be an eutectic tin-lead alloy a melting point of 456 [degrees]K. For the cone and hemisphere-cone models two distinct modes of melting were observed. In cases where the estimated equilibrium surface temperature (Tw)o was approximately equal to the material melting temperature Tm, melting occurred only at the stagnation point of the model and was such that a flat surface normal to the gas stream always resulted. If the average rate of heat transfer at the air-liquid interface be defined as qi = LmPm x, where Lm is the latent heat of fusion, Pm is the density of the material and x is the rate of recession of the flat surface, it is found that qi decreases with increase of the radius of the flat nose. A very approximate theory is found to show some agreement with the experimental rates of heat transfer. When (Tw)o was considerably greater than Tm the flat surface was no longer preserved and the resulting steady ablating shape was paraboloidal in nature. When this occurred x was usually constant. This allowed some average steady state heat transfer rates to be evaluated and compared with theory. Preliminary tests were also made with a two-dimensional wedge model.