Publisher Summary There are three approaches in the finite element analysis of vortex-induced vibration of bluff cylinders. In one approach, fixed finite element meshes are employed in association with velocity boundary conditions on the cylinder surface. Moving meshes are employed in the others. One approach is to translate variables to updated mesh. More sophisticated method in this approach has been recently proposed by Tezduyar, et al., who are developing deformable space-time element. The last approach is to employ the arbitrary Lagrangian-Eulerian (ALE) concept. Applications of the ALE concept to the finite element analysis of fluid-structure interaction problems can be found in early 1980s though its application to vortex-induced vibration of cylinders is reported only recently. This chapter discusses some numerical examples regarding the ALE finite element analysis of vortex-induced vibration of a bluff cylinder as well as computational techniques supporting such analysis.