A problem relevant to the study of machines and constructions, namely, the formation of a local deflected mode at the point of stress concentration with a forced deformation jump on a contact surface of composite construction elements and machines, is considered. The similarity/dimensional theory is used to analyze the deflection mode in the stress concentration region, i.e. in the neighborhood of an irregular boundary point. It has been shown that, in order to be represented as a power complex, the experimental data (orders of bands) in the neighborhood of an irregular point of the region boundary must, like stresses, possess the property of similarity. The obtained similarity criteria and dependences have been experimentally verified.