Newtonian (n = 1) and pseudoplastic (n = 0.8, 0.5) fluid flow over a rectangular cylinder placed near a plane wall (gap ratio G/a = 0.25 and 1) is studied numerically using Ansys Fluent when the body shape of the cylinder changes from a bluff body (aspect ratio, AR = 1) to an elongated body (AR = 4). The study shows that body shape of the cylinder and pseudoplasticity of the fluid play pivotal roles to change the flow field variables along with aerodynamic forces for a relatively high gap ratio (G/a = 1, respectively). \(\overline{C}_{{\text{L}}}\) increases and \(\overline{C}_{{\text{D}}}\) reduces with increase in AR value of the cylinder. With high pseudoplasticity in fluid flow (n = 0.5), this trend becomes more prominent. Also for n = 0.5, multiple values of Strouhal number (St) are obtained for cylinder with low AR (AR = 1) at a large gap ratio (G/a = 1). When the rectangular cylinder is kept very close to the plane wall (G/a = 0.25), vortex suppression occurs irrespective of cylinder size or flow nature which negates the changes in the flow field and aerodynamic forces.