The single-degree-of-freedom flow-induced vibration of three elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement at low Reynolds numbers was numerically investigated by using a semi-implicit characteristics-based split (CBS) finite element algorithm.The influences of some key parameters, such as Reynolds number (Re), shear ratio (k), and reduced velocity (Ur) on the characteristics of transverse dynamic responses, hydrodynamic coefficients, phases, spectrums and wake modes of three circular cylinders with tandem arrangement were analyzed.The numerical results show that with the increasing of Re the maximum amplitudes of three cylinders increase and a great difference between the amplitude beyond the resonance regime of midstream and downstream cylinders under different shear ratios is observed.The vibration amplitude of three cylinders versus the shear ratio can be divided into several stages respectively under different Re.The maximum value of drag and life coefficients of the downstream cylinder are more sensitive to the increasing of Re, and the influence of k on the hydrodynamic coefficients of the midstream and downstream cylinders concentrates on the r.m.s.value of the lift coefficient in the resonance and greater reduced velocity regime.With the increasing of Re and k, the range of the phase switch and its subsequent recessed segment broadens obviously.Moreover, the order of the frequency in PSD of the lift coefficient and transverse displacement and the energy corresponding to the main frequency show a significant change.Affected by the incoming flow velocity difference and inertial effect, a large irregularity was observed in the wake modes of the three cylinders.