Actual concentrated stress distributions at a notch front in Si_3N_4 were measured by the collimated X-ray sin^2Ψ method and validated by the fracture mechanics. The elliptic model expresses well the features of stress distributions at U and V notch front which is analyzed with their finite length and tip radius. The stress intensity factor, K_I, can be obtained experimentally from the measured stress distribution plotting versus characteristic function in the elliptic model. An apparent stress singularity was observed to be -0.5 in the range 0.05-0.5 mm from the tip, but the elliptic model also provides a similar linear tendency.