Alfvén eigenmodes (AEs) with toroidal mode number n = 0 (i.e., axisymmetric) have been observed in the ellipticity-induced frequency range in the Joint European Torus. The axisymmetric modes are of interest because they can be used to diagnose fast particle energy distributions at the mode location. The modes were identified as global Alfvén eigenmodes (GAEs), with the ellipticity of the plasma cross-section preventing strong continuum damping of the modes. The MHD codes CSCAS, MISHKA, and AEGIS were used to compute the n = 0 Alfvén continuum, eigenmode structure, and continuum damping. For zero ellipticity, a single mode exists at a frequency below the Alfvén continuum branch. This mode has two dominant poloidal harmonics with poloidal mode numbers m = ±1 that have the same polarity; therefore, it is an even mode. For finite ellipticity, the continuum branch splits into two branches and the single GAE splits into two modes. An even mode exists below the minimum of the top continuum branch, and the frequency of this mode coincides with the experimentally observed AE frequency. The other mode is found below the lower continuum branch with opposite signs between the two poloidal harmonics (an odd mode structure). This mode was not excited in our experiment. Analytical theory for the n = 0 GAE in an elliptical cylinder shows the n = 0 Alfvén continuum agrees with the numerical modelling.