The lowest natural frequencies of thin-walled noncircular fiber-reinforced composite cylinders, specifically cylinders with elliptical cross sections, are investigated. Of interest is the variation of the lowest natural frequency, the so-called fundamental frequency, as a function of wall laminate properties, cross-sectional eccentricity and other cylinder geometric parameters. Both simple and clamped support boundary conditions are investigated. Laminate properties that are uniform with circumferential location and laminate properties that vary with circumferential location, by way of varying laminate fiber angle with circumferential location, are considered. As the radius of curvature of a noncircular cylinder varies with circumferential location, it is logical to consider the influence of circumferentially varying fiber orientation on the fundamental frequency. The analysis for predicting the fundamental frequency is based on Donnell shell theory, linear elastic properties, and the use of Hamilton's Principle in conjunction with the Rayleigh-Ritz technique. By use of a so-called shape factor, the magnitude of cylinder normal displacements are modulated to be larger in the regions of the cross section with the largest radius of curvatures and smaller in the regions with the smallest radius of curvature. The final equations for predicting the fundamental frequency are quite complex, but a series of approximations results in a hierarchy of simpler equations, the simplest being referred to as Lo's approximation. The prediction of the fundamental frequencies is spot checked by comparing the results as predicted by the various levels of approximation with predictions of a shell-based finite element model. Considering uniform laminate properties, comparisons between the developed analysis and the finite element model are good for all levels of simpler equations, and excellent in some cases. The developed analysis is subsequently used for parameter studies. It is found that compared to a circular cylinder of the same circumference and with uniform laminate properties, the fundamental frequency of an elliptical cylinder is always less. Surprisingly, based on the results obtained, it appears that for a given cylinder geometry the fundamental frequency is not particularly sensitive to wall lamination sequence, though the wave number in the circumferential direction of the mode shape associated with the fundamental frequency is sensitive to lamination sequence. Considering cylinders with circumferentially varying fiber orientation, comparisons between the developed analysis and the finite element model for most of the cases studied are good. However, the developed equations are limited since it is difficult to find a set of known functions to describe the deformation of an arbitrary lamination sequence when applying the Rayleigh-Ritz technique. In general, in can be concluded that the effect of varying fiber orientation on the fundamental frequency is much less than the influence of cylinder aspect ratio. It can also be concluded that the developed analysis would be an excellent tool for design purposes, as the calculation of the fundamental frequency is done quickly, and design trade-offs studies would be easy. / Ph. D.