In this report, the extension-torsion coupled vibration behavior of several structural members is investigated. In order to solve the governing differential equations of motion for the problem, three different approaches, namely the dynamic stiffness matrix (DSM), finite element (FEM), and dynamic finite element (DFE) methods are used. Three different engineering applications of interest are identified, namely, a helical spring, a wire rope and laminated composite beams. For each of these applications, a method for determining the cross-sectional stiffness constants of interest is first introduced. Illustrative examples of each system are then studied where resulting natural frequencies and modes are compared to those available in literature. In order to determine the performance of each solution method in the determination of the dynamic behavior of these systems, all three (DSM, FEM, and DFE) methods are used in the examples, and a comparative study among the results is then carried out to gauge the accuracy of each approach.