The Griffith criterion for fracture of brittle materials is based on a model of a continuum in which infinitely sharp cracks are distributed with random orientations. This study extends the Griffith analysis to cracks of finite sharpness. While the Griffith criterion predicts a compressive strength of eight times the tensile strength, the extended criterion predicts a compressive strength of any value from three to eight times the tensile strength depending on the sharpness of the cracks. To test the validity of the extended criterion, tests were conducted on porous zirconia under ratios of compressive to tensile stress of 0, 3, and 5, and under compressive stress. A specimen was designed and test procedures developed so that the average bending stress was 1.99 percent. A test program was designed so that a statistical confidence limit could be assigned to the test results. The test results of the proposed criterion fell within a 99 percent confidence band, while all other criteria fell outside of the band for many combinations of tensile and compressive stress. The average compressive strength of the porous zirconia was approximately 7.1 times the tensile strength.