Using a Green’s function approach with a dipole formulation, it is possible to find the shape of a two‐dimensional steady Taylor bubble satisfying Bernoulli’s equation. This is done for the case of bubbles rising in a vertical channel. Our inviscid treatment leads to an infinite set of shapes. Using experimental evidence, however, it is possible to obtain one shape and a comparison with experiments is presented. The potential bubble so chosen has the distinction that it is the only one in the family of potential curves with a circular nose. An integral mass and momentum balance analysis in the liquid region between the free surface and the walls is also conducted, which takes fluid viscosity into account. By requiring a match between the two techniques at the nose, a viscous bubble is obtained that agrees well with both the potential bubble and experiments.