Design/methodology/approach - The governing equations of fluid flow over the elliptic cylinder are solved numerically on a Cartesian grid using Projection method based Immersed Boundary technique. This numerical method is validated with the results available in open literature. This scheme eliminates the requirement of generating a new computational mesh upon varying any geometrical parameter such as AR or AOA, and thus reduces the computational time and cost.Findings - Different vortex shedding patterns behind the elliptic cylinder are identified and classified using time averaged centerline streamwise velocity profile, instantaneous vorticity contours and instantaneous streamline patterns. A parameter space graph is constructed in order to reveal the dependence of AR, AOA and Re on vortex shedding. Integral parameters of flow such as mean drag, mean lift coefficients and Strouhal number are calculated and the effect of AR, AOA and Re on them is studied using various pressure and streamline contours. Functional relationships of each of integral parameters with respect to AR, AOA and Re are proposed with minimum percentage error.Practical implications - The results obtained can be used to explain the characteristics of flow patterns behind slender to bluff elliptical cylinders which found applications in insect flight modeling, heat exchangers and energy conservation systems. The proposed functional relationships may be very useful for the practicing engineers in those fields.Originality/value - The results presented in this paper are important for the researchers in the area of bluff body flow. The dependence of AOA on vortex shedding and flow parameters was never reported in the literature. These results are original, new and important.Purpose - The purpose of this paper is to study the effects of Angle of Attack (AOA), Axis Ratio (AR) and Reynolds number (Re) on unsteady laminar flow over a stationary elliptic cylinder. © Emerald Group Publishing Limited.