The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure along one direction tangent to the shell midsurface. The aim of this paper is to propose a new averaged nonasymptotic model of such shells, which makes it possible to investigate free and forced vibrations, parametric vibrations, and dynamical stability of the shells under consideration. As a tool of modeling we will apply the tolerance averaging technique. The resulting equations have constant coefficients in the periodicity direction. Moreover, in contrast with models obtained by the known asymptotic homogenization technique, the proposed one makes it possible to describe the effect of the period length on the overall shell behavior, called a length-scale effect.