Flow-induced vibration of two circular cylinders in tandem arrangement elastically mounted with a mass-spring-damping system was studied by solving the primitive variable Navier-Stokes equations incorporating the Arbitrary Lagrangian-Eulerian (ALE) method. The convection term and dissipation term were discretized using the third-order upwind compact scheme and the fourth-order central compact scheme, respectively. The typical spacing between the cylinders is 4 diameters, which is close to the critical value. The dynamic response of the vibrations on two cylinders with two-degree-of-freedom motion is different from that of an isolated cylinder, and also different from that of a cylinder vibrating in the wake of a fixed upstream one. Different flow patterns were found in the wake, and proved to be relevant to the discontinuities observed in the response of the oscillatory cylinders. Flow-induced vibration of two circular cylinders in tandem arrangement elastically mounted with a mass-spring-damping system was studied by solving the primitive variable Navier-Stokes equations incorporating the Arbitrary Lagrangian-Eulerian (ALE) method. The convection term and dissipation term were discretized using the third-order upwind compact scheme and the fourth-order central compact scheme, respectively. The typical spacing between the cylinders is 4 diameters, which is close to the critical value. The dynamic response of the vibrations on two cylinders with two- degree-of-freedom motion is different from that of an isolated cylinder, and also from different from that of a cylinder vibrating in the wake of a fixed upstream one. Different flow patterns were found in the wake, and proved to be relevant to the discontinuities observed in the response of the oscillatory cylinders.