The stability of an axisymmetric tandem mirror to ballooning modes is examined including the effect of finite ion gyroradius stabilization. The central cell of the tandem mirror is treated as a long‐thin system with isotropic pressure, while the end plug is modeled by a stabilizing boundary condition. For the particular equilibrium considered, the finite Larmor radius corrections to ideal magnetohydrodynamic theory indicate a strong stabilizing effect on high–nballooning modes even for quite modest values of the gyroradius,k⊥ &rgr;i∼a/L≪1. The dependence of &bgr;conk⊥ &rgr;iis computed, and physical mechanisms associated with this stabilizing influence are discussed.