The damage mechanisms of α-zirconium polycrystals in tension at room temperature and their dependence on texture and grain size are investigated. Ductile damage proceeds by growth of cavities appearing at triple nodes; at larger strain, other cavities nucleate at precipitate platelets. The cavitation kinetics depend on the tension direction; they are lower the coarser the grains. For a better understanding of the cavity formation at triple nodes, the internal stress field due to intergranular plastic incompatibility is estimated. The mean stress exhibits a logarithmic singularity on the triple junction. By combining this property with some experimentally determined features of the cavity growth (tubular shape along the c axis and growth by activation of prismatic glide), a crystallographic orientation-dependent cavitation criterion is derived. The determination of the grains orientation by the E.B.S.D. technique leads to a satisfactory comparison of the model predictions with the observations.