We used a continuum model to investigate the isochoric radial expansion of a right circular cylindrical specimen composed of a nematic elastomer that is crosslinked in a uniaxial state and then annealed. Numerical solutions show that, above a certain radial expansion, the material has a definitive energetic preference for a state involving a disclination of strength +1 along the cylinder axis. Surrounding such a disclination is a core with radial dimension on the order of 10(-2) mum, which coincides with observations in conventional liquid-crystal melts. Examination of the normal-stress differences indicates that the first of these differences depends nonmonotically on the extent of radial expansion and possesses a local minimum at the point where a disclination becomes energetically preferred. This suggests a practical experimental method for testing the predictions of our model.