Modern air traffic control systems in airports use high-speed ground tracking radars usually rotating at 60 rpm. The flow induced vibration and noise generation of the newly developed radar antennas are the two serious problems that jeopardize the successful deployment of the new ground aircraft tracking systems. The present study is an attempt to understand the viscous flow characteristics around a typical radar antenna cross section via computations. After a steady-state validation of the computations, a parametric study of possible new shape designs for the antenna is discussed. The present computations are validated by using a well-known experimental data set for a cylinder in cross flow, at the operational Reynolds number of 426,000. The predicted drag coefficient for the cylinder agrees well with the measured CD values. Significant aerodynamic drag reductions via careful shape design of the antenna are possible. Elongating the original antenna cross section in the chordwise direction by keeping the antenna height constant is an effective aerodynamic solution for further drag reductions.