The response characteristics of beams and plates made from composite laminates are strongly affected by the shear deformations of their layers. However, incorporation of the shear deformation further complicates the equations of motion and their analysis. As a result the vibration analysis of such structures have been limited to simple free vibration studies such as determination of their frequencies. The forced vibration problems of these structures have been solved by exact methods for only some very simple cases. In this study, a generalized modal approach is presented to solve more general vibration problems of composite beams and plates. The coupled systems of partial differential equations, representing the equations of motion, are uncoupled into modal equations by utilizing the eigenfunctions of the system and its adjoint. A method is presented to obtain these eigenfunctions for beams with arbitrary boundary conditions and for plates with Levy-type boundary conditions. The forced vibration solutions obtained by this method are then used to calculate the random response characteristics of beams and plates subjected to spatially and temporally correlated random loads. In the analysis of beams, both symmetric cross-ply and angle-ply configurations have been considered. In the symmetric cross-ply configuration with no torsional loads, of course, the warping effects are absent. The angle-ply case, however, includes torsion-warping effects and coupled bending-torsion motions. A simple displacement field is introduced to reflect warping in the third-order shear deformation theory. In the analysis of plates also two configurations of the laminates have been considered: symmetric cross-ply and antisymmetric angle-ply. At this time, these are the only two configurations which can be solved by the closed-form modal analysis approach for the Levy-type boundary conditions. In both cases of the beams and plates, the numerical results with and without shear deformations are obtained and compared. The results for no shear deformation are obtained with the classical lamination theory. The results have also been obtained for the first-order shear deformation theory with a somewhat simpler displacement field which has been commonly used in the past by several investigators. The numerical results are obtained for the global response quantities such as frequencies, displacements and crossing rates as well as for the local response quantities such as normal and shear stresses across a cross section. The numerical results obtained with various deformation theories for the frequencies as well as response quantities are compared to evaluate the effect of the shear deformations. For thicker and rigid beams and plates, one observes large differences in the frequencies and responses obtained with (the first- and third-order shear deformation theories) and without consideration of shear deformations (classical theory). For the frequencies and global responses both the first- and third-order theories give about the same results. But for the local response quantities, the results obtained with the two shear deformation theories can also be quite different in some cases. In any case, the results clearly point out the importance of including the shear deformations in thick and rigidly constrained composite beams and plates. Although, in this study only uniform cross section or uniform thickness beams and plates have been considered, it is felt that the eigenfunctions developed herein can also be conveniently utilized with advantage as comparison functions in approximate Rayleigh-Ritz type of approaches to analyze non uniform structures. / Ph. D.