Abstract: The convective outflow boundary condition is used in the multistep characteristic-based operator-splitting(MCBOS) finite element method. A numerical model for linear shear flow past square cylinders in tandem arrangement is established. The model is proven feasible through the simulation of the linear shear flow past isolation square cylinder. Effect of the shear parameter and spacing ratio has been studied. The numerical results show that the shear flow can suppress vortex shedding and decrease the S_r number. The stagnation point of the upstream square cylinder shifts toward the lateral separation point. When shear parameter is equal or greater than 0.3, the location of the stagnation point remains unchanged. The results also show that the wake field of the gap of two tandem square cylinders changes from the steady state to the unsteady state without vortex shedding and then to the unsteady state with vortex shedding as the spacing ratio increases. The reason for this in deeply connects with the continuous negative value. The dramatic increase in the pressure difference between stoss and lee side leads to increased the mean drag coefficient abruptly.