The fluid in motion exerts force on the solid body immersed in it such as flow around an airplane, automobiles and underwater pipelines. The flow around a cylinder near a flat plate boundary layer can be related to an upward force on the aircraft during landing. This ground effect phenomenon is often characterized by an increase of lift accompanied by drag force reduction. It depends on the flow velocity, surface body roughness, body orientation immersed in the fluid with the direction of fluid flow and the object configuration. A numerical investigation is carried out using ANSYS Fluent. Two-dimensional unsteady Navier-Stokes equations are solved using finite-volume method with second-order accuracy for spatial and fourth order for temporal schemes. A detailed grid-independent test is carried out and the numerical results were validated against available experimental values in the literature. The present study illustrates the flow field evolved and the wake-boundary layer interaction when flow past a circular and elliptical cylinder at Reynolds number (Re-D) 40 and 1000, where D denotes the diameter. The interaction of shed vortex developed with the flat plate boundary layer is predominant for a circular shaped cylinder when compared to an elliptical one. This event becomes less prevalent as the gap to diameter ratio increases. The results demonstrate shear layer formation, its shedding, its interaction with the boundary layer, etc.... The varying non-dimensional frequency, lift and drag coefficient along with the iso-contours of vorticity show the influence of gap ratio on the modification of wake dynamics and evolution of the wall boundary layer. For low gap ratio, it appears that the wake-boundary layer interaction becomes less prevalent as the shape changes from circular to elliptical. It is observed that for a higher gap to diameter ratio, this interaction becomes less prevalent for both circular and elliptical cylinders.