The magnetohydrodynamic (MHD) ballooning stability of the TJ-II heliac standard configuration is examined using a criterion derived for three dimensional (3-D) general configurations. From the ideal limit of this criterion, a critical ⟨β⟩ approximately=1.3% is obtained. This critical value is very close to that obtained from the Mercier criterion and is almost unaffected when those terms associated with compressibility are retained. The inclusion of resistivity is shown to have almost no effect on the attainable critical ⟨β⟩ even though unstable modes persist for lower ⟨β⟩ values due to their small growth rate. For parameters relevant to this configuration, the resistive pressure convection limit predicts unstable modes, scaling as γ~m2η for all ⟨β⟩ below the ideal limit, which are shown to disappear when compressibility terms are retained in the calculations. Unstable resistive ballooning modes with γτ A~10-3 are then found for ⟨β⟩ values down to 90% of the ideal critical ⟨β⟩. The growth rate rapidly falls if the pressure gradient is further decreased owing to the stabilizing effect of compressibility for γτA << 1