Penalty finite‐element solutions have been obtained for steady uniform flow from the left to the right over a clockwise rotating circular cylinder near a plane wall. Results are presented for Reynolds numbers 20 and 40, the non‐dimensional speed of rotation of the cylinder 0.0 ∼ 0.5 and the gap between the plane wall and the cylinder surface 0.2 ∼ 4.5 times the diameter of the cylinder. The motion is assumed to be two‐dimensional and to be governed by the Navier‐Stokes equations for incompressible fluids. The finite element approach is utilized and the frontal method is used to solve the stiffness matrix. In the cases of the cylinder without rotation, the results show that when the gap is large(H>2D), the effect of the wall makes the pressure on the cylinder surface decrease, andCl, CdandCtincrease. When the gap becomes small(H <2D), it makes the pressure andClincrease, andCtandCddecrease. For the gapH <0.7D, a recir‐culation zone is formed on the plane wall behind the cylinder. The smaller the gap, the recirculation zone is closer to the cylinder. The average rate of variation ofClandCdforH <1D isabout ten times those forH >1D.