The existence of steadily translating vortices in a semi‐infinite barotropic fluid stratified by a constant gravitational field is considered. Assuming that the flow field of the vortex is subsonic and contains finite total kinetic energy, it is found that steadily translating vortices do not exist in three dimensions, but do exist in two dimensions. An analogy between a subsonic, barotropic, stratified fluid, and a uniform fluid with a free‐slip planar boundary is exploited to show that the same result applies in a semi‐infinite uniform fluid. ©1995 American Institute of Physics.