Vortex-induced vibration (VIV) is very significant in influencing the structural safety of many practical engineering applications. However, the VIV mechanism of multiple elastically coupled cylinders is poorly understood. In this paper, the VIVs of two elastically coupled cylinders in a side-by-side arrangement is numerically studied under different effects, including the stiffness ratio of the two springs (K2/K1), the diameter ratio of the two cylinders (D2/D1), and the Reynolds number. The mass ratio of the two cylinders is 1.92. K2/K1 and D2/D1 have a significant impact on the maximum vibration amplitude and vibration frequency of the two-cylinder system. Furthermore, unlike the resonance of a single cylinder, no frequency-locking phenomenon occurs. When the Reynolds number is constant, it is found that the changes in K2/K1 and D2/D1 change the natural frequency of the system, and the lift force coefficient (CL) of the cylinders and the phase between the lift force and displacement (φ) change accordingly. The maximum vibration amplitude of a cylinder is proportional to the parameter CLsinφ. Under certain frequency conditions, the amplitude of one cylinder is significantly suppressed. In addition, when the natural frequency of the system is fixed, the Reynolds number also changes the CL and φ of the cylinders. Therefore, the method of suppressing the vibration of one cylinder by coupling the other cylinder in parallel is severely restricted by the Reynolds number. The conclusion of this study has certain guiding significance for the structural design of dual submerged floating tunnels with elastic connections.