1. A method was worked out for the highly accurate measurement of arrays of displacements by the method of speckle photography. The displacement fields were determined innotched specimens loaded by three-point bending. The error of measurement does not exceed 1.5%. 2. Algorithms for processing the data of speckle photography and of calculation of J-integrals from them were worked out and verified on computer models. A numerical analysis of the statistical characteristics of the smapling distributions of J-integrals taking account of the random errors of measurement by the method of speckle photography was carried out. 3. A large number of measurements and high accuracy permitted the conclusion that the J-integral is invariant for elastoplastic specimens with 5% significance level. Differences in the behavior of elastic and plastic specimens were registered in the displacement fields, in the sampling distribution, in their statistical characteristics, and also directly in the great variability of the J-integrals for plastic specimens.