Abstract The analysis of corrugated shells (plates) is based on the assumption that they can be analyzed as thin, equivalent orthotropic shells of uniform thickness. The analytical expressions for the equivalent rigidities of orthotropic thin shells given in the literature are reviewed. The results of a finite element analysis of a corrugated sheet subjected to constant strain states reveals an inadequacy in some of the classical expressions in use today. These equivalent orthotropic properties are improved with the derivation of new expressions. In addition, expressions for the localized stress concentrations developed at the ridges of the corrugations are derived.