A tokamak’s economic performance is strongly affected by the plasma pressure that it may sustain, which in turn is limited by the maximum pressure gradients that may be supported. Ballooning modes are typically driven unstable by increasing the pressure gradient, and because they can radially extend across many rational surfaces, they can seriously reduce a plasma’s energy confinement. Here an eigenmode formulation is used to study the stability of ballooning modes in internal transport barriers (ITBs), in which very strong pressure gradients and flow shears may be found. This extends previous studies that used an ‘eikonal’ formulation, as it enables the study of: ballooning modes with a finite toroidal mode-number n (finite wavelength perpendicular to the magnetic field), to find new solution branches, to obtain the eigenmode structures, and to investigate the effects of a radially varying equilibrium.