In this work, an historical overview concerning the theory of shell structures is presented. Early conjectures proposed by, among others, French, German, and Russian authors are discussed. Moreover, considering a recent approach in the field of structural analysis, based on the static–kinematic duality concept, static and kinematic matrix operator equations are formulated in the case of shells of revolution, emphasizing how these operators are one the adjoint of the other. In this way, any possible inaccuracy provided by the previous approaches can be overcome.