This chapter discusses the topics of longitudinal, torsional, and flexural vibrations with and without elastic media as well as coupling vibration. Flexural vibration further involves deformations due to bending and shear, rotatory inertia, and P-Δ effect. Coupling vibration herein implies that a structure vibrates in longitudinal and flexural modes, torsional and flexural modes, and longitudinal, torsional, and flexural modes. The effects of various parameters on vibration, such as the influence of bending and shear deformations, rotatory inertia, elastic media, and axial force on flexural frequencies, are derived in a closed form expressed in partial differential equations which are then used to obtain dynamic stiffness coefficients. The chapter provides numerical examples which are not only to illustrate calculation procedures but also to show the significant effects of coupling vibration and parameters on structural response. When a plane structure is subjected to dynamic excitations, its constituent members may have longitudinal and flexural vibration. The vibration modes and frequencies may be coupled.