The inverse problem of reconstruction the crack-size distribution function from the amplitude-frequency acoustic emission spectrum is considered. It is shown that this problem can be solved with the use of the models proposed in this work for the dependence of the averaged difference of elastic stresses at the surfaces of radiating cracks on their radius. The proportionality coefficients of these dependences are fitted by minimizing the free surface energy, i. e., by searching for the minimum of the specific internal surface of cracks with a constant crack volume (porosity).