The strain to failure of a transversely loaded composite is much lower than for the pure matrix in uniaxial tension. Several studies of composites suggest the triaxial matrix stress state as one of the explanations. In order to investigate this experimentally, a triaxial tensile test previously used for rubbers (the poker-chip test) was successfully applied to four epoxies in the glassy state. The chosen specimen geometry mimicked the most severe stress state in the matrix as determined by finite element analysis of a transversely loaded glass-fiber/epoxy composite. The poker-chip strains to failure in the primary loading direction were 0.5-0.8%, whereas uniaxial strains to failure were 1.8-7%. The triaxial stress state in composite matrices may therefore by itself be a sufficient explanation for low values of transverse composite strains to failure.