A comparative fractal analysis, about the mechanical aspects of the freezing phenomenon, in tissue (t = -30°C; t= -70°C) has been performed over the diaphragm muscle. Starting with the classical one, recalling the Stefan model we justify the no-smooth interface between soft and hard phases. So, we translate the problem as the contact problem applying the relative computational methods about the stress distribution in the contact neighbour. Fractal dimension of the interface structures increased with the lowest temperature (p<0.001), permitting to obtain an accurate quantification of the tissue damage after freezing, an important features to study effectiveness and reality of the models.