A new method of obtaining a dispersion equation for ballooning flute modes in a tokamak is proposed. The author derives a generalized dispersion equation for these modes in a tokamak with circular magnetic surfaces and an arbitrary pressure profile. It is shown that this equation behaves differently in the s > 1/2 region and in the region with s < 1/2, where s = (1/4 + Uo)1/2 − 1/2, and Uo is the Mercier coefficient. It is established that the stability limit for ballooning flute modes strongly depends on the plasma pressure profile. Finally, the author demonstrates that the plasma self-stabilizing effect can substantially improve the stability of the plasma against these modes.