High-speed injection of frozen hydrogen isotope pellets is considered by many to be the most effective method of fueling tokamak plasmas. In the plasma environment the pellet disintegration time could be extremely small, placing stringent requirements on the injection speed and the technology of fuel injection. Several models concerning the composition and spatial extent of the ablation cloud surrounding the pellet have been employed, and they have produced widely varying results for the ablation rate. Most, if not all, of these models have relied on spherical geometry to represent the ablation cloud, although in some instances the effects of the magnetic field on the energy flux reaching the pellet have been taken into account and have resulted in an adjustment of the ablation rate by a “flux reduction factor.” The geometric effects on ablation are examined by assuming the ablation surfaces to also be magnetic flux surfaces. Such an assumption is perhaps most natural for nonspherical geometry especially since there is some basis for it in the experimental observations. It is found that such geometric considerations could lead to sizable reductions in the ablation rate. It is also confirmed that the effects of the magnetic field on the ablation rate are not particularly significant.