In this thesis both static and dynamic analyses of composite thin-walled structures are carried out. Most notably, the Dynamic Stiffness Method (DSM) has been extensively exploited to develop advanced formulations for plates and shells. In particular, the. Dynamic Stiffness (DS) matrices have been developed for laminated composite plates and shells using Higher-order Shear Deformation Theory (HSDT) in order to investigate their free vibration behavior and buckling characteristics. First, the Governing Differential Equations (GDEs) of motion and associated natural Boundary Conditions (BCs) (Neumann-type) for the given displacement field are derived via Hamilton's principle for both composite plate and shell structures. In the case of composite plates, the DS matrices are formulated for both out-of-plane and in-plane deformations. The GDEs for each of the two cases are solved in Levy's form separately. Next the problems for both plates and shells are reduced to a system of ordinary differential equations which are then solved by using the classical exponential solution procedure.