Аннотация:The parametrization of the domain occupied by a shell in the three-dimensional Euclidean space by using several base surfaces permits one to describe more accurately the variation of the stress-strain state of the shell structure across thickness. For this reason, this parametrization has an advantage over the classical one for describing multilayer shell structures, including thick shells. In analyzing multilayer shell structures, one can use the face surfaces of the layers as the base surfaces, which takes into account more adequately the nature of contacts between the layers. In what follows, the general analysis of the parametrization suggested is presented. We also consider the construction of the theory of multilayer structures which is generated by this parametrization.