Mean and fluctuating surface pressure data are presented for a square cylinder of side length D placed near a solid wall at Re-D=18,900. One oncoming boundary layer thickness, delta=0.5 D was used. Measurements were made for cylinder to wall gap heights, S, from S/D=0.07 to 1.6. Four gap-dependent flow regimes were found. For S/D>0.9, the flow and the vortex shedding strength are similar to the no-wall case. Below the critical gap height of 0.3D, periodic activity is fully suppressed in the near wake region. In between, for 0.3<S/D<0.9, the wall exerts a greater influence on the flow. For 0.6<S/D<0.9, the mean drag and the strength of the shed vortices decrease as the gap is reduced, while the mean lift towards the wall increases. Evidence is presented that for S/D>0.6 the influence of the viscous wall flow in the gap is not dominant and that, consequently, inviscid flow theory can describe changes in the mean lift as S/D decreases. For 0.3<S/D<0.6, the flow reattaches intermittently on the bottom face of the cylinder and viscous effects become important. Below the gap height of 0.4D, periodic activity cannot be observed on the cylinder.