A more accurate dispersion equation for ideal ballooning flute modes in a plasma with alpha particles is obtained. It is shown that circulating and trapped alpha particles generate the eigenbranches of the mode oscillations with frequencies ω ≲ ω*i, where ω*i is the ion drift frequency. The relevant growth rates and frequencies are found. It is ascertained that in the frequency range , where is the magnetic drift frequency average over a bounce period, trapped alpha particles may generate forced oscillations that influence the ideal ballooning flute mode stability boundary. It is shown that the stability may be improved for certain plasma parameters and trapped alpha-particle pressures.