A numerical study is made of the shear flow past a square cylinder (of height A*) near a wall (at a gap height 0.5A*) in presence of a vortex generating upstream rectangular cylinder (of different heights a* and widths b*) placed at a fixed height 1.25A* in an offset tandem arrangement. Influence of fluctuating aerodynamic forces of the vortex generator (VG) on the downstream cylinder (DSC) is investigated based on parameters: spacing between the cylinders S(=D*/A*), ratio of heights r2=a*/A* (≤1), aspect ratio r1=b*/a* (≤1) and Reynolds number Re (based on A*). A formula is derived for local Rel=Re×(L+r2/2)×r2 to calculate the effective Re for the VG placed at height L. The critical Reynolds number Rer1-1.25 (at which the VG of r1=0.1, 0.5 and 1.0 starts to shed the vortices) is predicted (using the formula for Rel and the Lagrange interpolation based on the previous data for single cylinder) and validated in the present study of tandem arrangement. A linear relation between Rer1-1.25 and r1 is established to predict Rer1-1.25 and finally a region of finite volume in the r1ReS-space (for the values of r1, Rer1-1.25 and critical spacing Scr for fixed value of r2) is proposed in order to generate the unsteadiness in the steady flow of the DSC at lower Re. The governing unsteady Navier-Stokes equations are solved numerically through a finite volume method on a staggered grid system using QUICK scheme for convective terms. The results for the present case of offset arrangement are compared with that for the case of inline arrangement highlighting some of the major issues: generating the vortices by the VG, the appearance of multiple peaks in the spectra of fluctuating lift coefficient, and the deviation of the aerodynamic characteristics of the DSC from that of the isolated square cylinder. © 2016 Elsevier Ltd.