Failure modes of polycrystalline alumina in compact-tension specimens were studied using the scanning electron microscope. Microcrack propagation was monitored under large magnification. Starting with a preexisting chevron notch, it was found that cracks propagated in a branching manner along the boundaries, that is, intergranular fracture occurred. Based on these experimental observations, a finite-element method was developed based on continuum damage mechanics. A Voronoi diagram was used to generate realistic grain structure for alumina. Numerical analysis of a specimen under pure tension was conducted to show similar features of crack propagation. The effects of different damaging rates for the bulk and shear moduli on peak stress and softening are given. It is shown that the combination of reduced damage of the shear modulus and the restriction of tortuous cracking along grain boundaries results in a significant enhancement of strength in the composite ceramic over the material strength in the grain boundary.