Experiments and theory concern the behaviour of a small bubble carried through an orifice by a very viscous liquid. The liquid was polybutene oil, of viscosity about 70 Pa s, i.e. 70,000 times that of water. The Reynolds number of the flow is substantially less than one, hence the flow pattern is approximately radial flowing into, and away from, the orifice. These flow patterns have profound effects on the shape of an entrained bubble. On the upstream side, the acceleration of the liquid, as it approaches the orifice, causes elongation of the bubble since the front of the bubble moves faster than the back. On the downstream side, the reverse occurs: the back of the bubble moves fast than the front. Thus the height of the bubble diminishes as it moves away from the orifice, leading to the formation of a ‘crescent-moon’ shape. The shape of these bubbles can be predicted by considering the motion of a droplet of the same liquid replacing the bubble: the resulting geometric theory gives good predictions of bubble deformation approaching the orifice and of ‘crescent-moon’ formation downstream of the orifice.