The failure envelopes of brittle honeycombs are affected by the cell-wall modulus of rupture. The variability in the cell-wall modulus of rupture is accounted for by assuming that it follows a Weibull distribution, giving the corresponding modulus of rupture for a prescribed survival probability. Furthermore, the existing model for the failure envelopes of honeycombs under in-plane biaxial loading is modified to take into account the effect of variability in the cell-wall modulus of rupture. Consequently, the failure envelopes of brittle honeycombs with a prescribed survival probability are developed. The effects of cell size, Weibull modulus and prescribed survival probability on the failure envelopes of brittle honeycombs are also evaluated.