This report is concerned with the calculations of the natural frequencies of an ideal structure somewhat representative of an aircraft fuselage. The results are based upon a simplified “shell” theory which permits proper allowance to be made for the shear stresses and the corresponding displacements. No use is made of the so-called “shear deflection”, but it is shown in the Appendix that, for the special case considered, this approach would yield the same answer. Numerical results are given in x7 and comparison is made with both the usual beam theory results and the frequencies calculated on the assumption that flexibility in shear is of primary importance.