Flow past an elliptic cylinder near a free surface at a Reynolds number of 180 is studied numerically by varying parameters such as the angle of attack (AOA), aspect ratio (AR), submergence depth (hS), and Froude number (Fr). The immersed boundary method and level set method are used to study the flow. Simulations are performed for elliptic cylinders with angles of attack varying as -45°, 45°, and 90° and aspect ratios 2 and 4. A detailed investigation of quantities like the Strouhal number and forces provides an understanding on the complex flow interactions between the free surface and the elliptic cylinder of varying AOA and AR. Variation in the angle of attack brings substantial changes in the flow and vortex shedding pattern. The most significant of all changes observed with different AOAs is related to vortex shedding suppression at a depth of 0.096. Vortex shedding is suppressed at an AOA = 45°, but at -45°, metastable states appear, and at 90°, partial vortex shedding suppression occurs. Varying AR, on the other hand, does not bring any significant changes in the flow features, except for variation in mean forces and the Strouhal number. © 2018 Author(s).