Many laser drilling applications require that the shape of the drilled hole be carefully controlled. In order to successfully do this it is necessary to understand the laser drilling process. This paper reports on a quantitative model which predicts the depth and shape of a hole drilled in alumina ceramic by a ruby laser. Both experimental and theoretical results indicate that the predominant drilling mechanism for this application is not one of surface absorption and conduction inward, but one in which laser energy is absorbed throughout the bulk of the ceramic. The depth and shape of holes drilled in ceramic have been accurately predicted from the measured beam energy density distribution. Finally, it is shown that the radiation pressure of the focused beam plays an important role in the romoval of molten material from the heated region.