Joukovskii’s model [J. Russian Physico. Chem. Soc.22, 19 (1891)] for a two‐dimensional bubble rising in an unbounded fluid is considered. This model approximates the wake behind the bubble by a region bounded by vertical walls. By using an inverse method, Joukovskii obtained an exact solution characterized by a Froude numberF=U/(gL)1/2= (2&pgr;)−1/2. HereUis the velocity at which the bubble rises,gis the acceleration of gravity, andLis the distance between the vertical walls. It is shown numerically that Joukovskii’s solution is not unique. When surface tension is neglected there is a solution for each value of 0<F<Fc, whereFc∼0.66. In addition there are solutions with a cusp at the apex of the bubble forF>Fc, and an isolated solution with a 120° at the apex forF=Fc. When surface tension is taken into account there is a discrete set of solutions. Each of these solutions corresponds to a different value ofF. As the surface tension tends to zero, all these solutions approach a unique solution. The numerical results indicate that this limiting solution is Joukovskii’s exact solution.