Ballooning modes in tandem mirrors with quadrupole vacuum field symmetry are investigated in the limits of zero gyroradius and large aspect ratio. The eigenmode equation derived from the guiding‐center energy principle is reduced to one dimension by the use of an eikonal representation of the cross‐field variation of the perturbation. The eigenvalue problem is solved numerically and the structure of the local dispersion relation examined in order to derive conditions for marginal stability. Applications to the TMX‐U and MFTF‐B tandem‐mirror experiments are presented.