The distribution of residual stress near the surface of ground ceramics is very steep. In the X-ray stress measurements of specimens with large stress gradient, the sin^2ψ diagram is nonlinear because of the change in X-ray penetration depth with X-ray tilt angle ψ. The stress measured by the X-ray method is a weighted average of the stresses over the X-ray penetration depth. However, the X-ray penetration depth has been taken rather arbitrary in the previous X-ray studies of steep stress distributions. In the present study, a steep stress gradient was generated in bending of a thin plate of silicon nitride of thickness 108 μm, and this applied stress was analyzed by the cosψ and parabola methods of X-ray measurement of stress gradient. The penetration depth is concluded to be infinite, and the range of the integral of the weighted average is from the surface of infinite depth. The thickness of about six times the effective penetration depth is enough to ensure the infinite range of integration. Several sources of errors in the measurement of stress gradient were discussed on the basis of numerical simulations.