Reversed shear Alfvén eigenmodes (RSAE) that were observed in the Joint European Torus (JET) P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987) and DIII-D J. L. Luxon, Nucl. Fusion 42, 614 (2002)] are studied with the ideal magnetohydrodynamic code NOVA-K C. Z. Cheng, Phys. Rep. 211, 1 (1992). It was found that the frequency behavior of the RSAEs can be described accurately by the NOVA-K code when plasma compressibility effects and toroidal plasma rotation are taken into account. For the mode activity on JET, the calculated drive exceeds the mode damping rate, consistent with experimental observations, while on DIII-D the growth rate from neutral beam ions for modes with high toroidal mode numbers is insufficient to account for the excitation of the modes and a major part of the drive comes from the background plasma.