Three epoxy systems of interest as composite matrix materials are examined for their yielding and failure behavior under uniaxial, biaxial and triaxial stress states. Yield criteria applicable to glassy polymers, i.e. accounting for the hydrostatic stress effect on the deviatoric stress to yielding, are assessed. It is found that under stress states resembling those in matrix constrained between fibers, e.g. equibiaxial and equitriaxial tension, yielding is suppressed while brittle failure, presumably caused by crack growth from cavitation, occurs. A criterion for this mode of failure is proposed as the critical dilatational strain energy density. Experimental data are found to support this criterion.