It is shown that the theoretical predictions and experimental observations of toroidicity-induced Alfvén eigenmodes (TAE's) are now in good agreement, with particularly detailed agreement in the mode frequencies. Calculations of the driving and damping rates predict the importance of continuum damping for low toroidal mode numbers and this is confirmed experimentally. However, theoretical calculations in finite-β, shaped discharges predict the existence of other global Alfvén modes, in particular the ellipticity-induced Alfvén eigenmode (EAE) and a new mode, the beta-induced Alfvén eigenmode (BAE). The BAE mode is calculated to be in or below the same frequency range as the TAE mode and may contribute to the experimental observations at high β. Experimental evidence and complementary analyses are presented confirming the presence of the EAE mode at higher frequencies. © 1993 American Institute of Physics.