Theoretical investigation is carried out to differ spectral density data of free oscillations of materials in the presence and the absence of cracks on the basis of which it is proposed testing data and polyfrequency method of NDT using mentioned data. New analytical expressions between estimates of spectral oscillation densities and minimum dimensions of cracks are received. Experimental test results of blades of gas turbine engine compressor in the presence and the absence of fatigue cracks which match with analytical results are presented.