Numerically simulated results are presented for shear flow past a square cylinder (of height A) near a wall (at a gap height 0.5A) in the presence of a family of upstream rectangular cylinders (of different heights a and widths b≤a) in an offset tandem arrangement (towards the wall) in order to investigate the physical mechanism for the cessation of vortex shedding from the downstream cylinder due to this arrangement and the dependency of the aerodynamic characteristics of the downstream cylinder on the operational dimensionless parameters, Reynolds number Re, gap height L from the wall, spacing distance between the cylinders S, ratio of heights r2=a/A (≤1) and aspect ratio r1=b/a (≤1). The governing unsteady Navier-Stokes equations are solved numerically through SIMPLE algorithm with the QUICK scheme for convective terms. The strong dependency of diversion of the flow (away from the narrow passage between the downstream cylinder×.