The vibration theory of cylindrical shells can be found in Flugge's book, also many papers have been published. However, most of these papers are not on the roof type but on the closed shape, excepting a few, such as Heki's approximate theory and Kunieda's exact but abridged expression of very tedious calculation caused by the singularity problems. So, to avoid those problems, using the potential function and introducing smoothly varying solutions, the exact theory for cylindrical shell roofs is formulated in Fourier series developed in longitudinal direction, and the lists of formulas for necessary quantities are presented in common forms.
