A mathematical model is proposed for studying the dynamic behavior of drillstrings, focusing on the lower section of the drillstring known as the bottom-hole assembly or "BHA". In parallel, a comprehensive assessment of existing concepts and techniques for addressing drillstring dynamics is undertaken. Accounting for stiffness, damping, and inertial properties of the BHA and by incorporating appropriate excitations and boundary conditions, the dynamic characteristics of the BHA can be analyzed. The representation of the BHA stiffness is influenced by the underlying beam formulation assumptions, the stress-stiffening effect of axial loads, the elastic properties of the various materials used in the BHA, and the effective stiffnesses of special BHA components with complex geometries. Damping in the BHA involves both internal structural damping and damping resulting from its interaction with the surrounding viscous drilling fluid. Damping for the structure is accounted for using recent damping data leading to a smooth damping function which involves the vibration frequency and the drilling fluid density. Inertial properties of the BHA include its mass and the added mass effects of the fluid, both inside and outside the BHA, which is displaced through its motion. Frequency response characteristics for the structure are developed assuming a monochromatic exciting force. Both damped and undamped responses are simulated using a transfer function representation developed by modal superposition techniques. Sensitivity studies are performed to determine appropriate grid spacing for specific BHA problems of interest. Parameter studies reflect the influence of fluid added mass, weight-on-bit, boundary conditions, and the location of the excitation force. Excitation mechanisms for actual drilling assemblies are studied leading to a response superposition procedure which fully accounts for the behavior of BHA in drilling operations. Topics for further research are recommended.