ESDU 78004 gives graphs that enable the lower natural frequencies of unstiffened shells to be predicted for a range of end conditions. Natural frequencies of initially unstiffened shells for flexural and torsional vibration are considered and the effect of an initial static load (axial@ circumferential or internal or external pressure) is taken into account by an adjustment to the frequencies for initially unstressed shells. Shell modal density data are also included for calculating shell response to a wide-band excitation. Worked examples illustrate the use of the data in practical situations. Data and programs for predicting the natural frequencies of stiffened shells and thick shells are provided respectively in ESDU 80040 and ESDU 81018. The program of ESDUpac A8040 may also be used to evaluate the flexural modes of thin-walled unstiffened shells.