Vortex-induced vibrations of three staggered circular cylinders are investigated via two-dimensional finite element computations. All the cylinders are of equal diameter (D) and are mounted on elastic supports in both streamwise (x-) and transverse (y-) directions. The two downstream cylinders are placed symmetrically on either side of the upstream body at a streamwise gap of 5D, with the vertical distance between them being 3D. Flow simulations are carried out for Reynolds numbers (Re) in the range of Re = 60-160. Reduced mass (m*) of 10 is considered and the damping is set to zero value. The present investigations show that the upstream cylinder exhibits initial and lower synchronization response modes like an isolated cylinder does at low Re. Whereas for both the downstream cylinders, the upper lock-in branch also appears. The initial and the upper modes are characterized by periodic oscillations, while the lower lock-in branch is associated with nonperiodic vibrations. The 2S mode of vortex shedding is observed in the near wake of all the cylinders for all Re, except for the upper branch corresponding to the downstream bodies. In the upper branch, both the downstream cylinders shed the primary vortices of the P+S mode. For the upstream cylinder, the phase between lift and the transverse displacement exhibits a 180° jump at certain Re in the lower branch. On the other hand, the downstream bodies undergo transverse oscillations in phase with lift in all lock-in modes, while the phase jumps by 180° as the oscillation response reaches the desynchronization regime.