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Computational-experimental methods are proposed to estimate the mode I and II stress intensity factors, to determine the stresses acting at the location of a crack before its initiation, and to find the coordinates of the crack tips. The initial data are displacement discontinuities measured at several points at the crack edges. The methods are based on integral representations of the solution of the elastic equilibrium problem for anisotropic plates with a curved cut. Numerical examples are given to illustrate the efficiency of the methods.