To accommodate multimedia wide-band operations at Ka-band (e.g., 30 GHz) are attracting much attention in both wireless terrestrial and satellite communication systems. With handset antennas operating at these frequencies, significantly high-peak specific absorption rate (SAR) may occur in the skin region of the human head, It has been found that the popular numerical techniques have severe computational limitations in dealing with thin layers and high frequencies. In order to critically assess human-antenna interactions at Ka-band, an efficient hybridization of the eigenfunction expansion method (EEM) and the method of moments (MoM) has been utilized. At this frequency band, most power absorption of the antenna-radiated power occurs within the thin layer of skin, With a half-wave dipole antenna separated at 2 cm from the head, it is found that the unaveraged peak SAR can become extremely high in the skin tissue (similar to 450 W/kg) with 1 W of the delivered power, while the 1-g averaged peak SAR is similar to 10 W/kg. However, the use of a directional two-element end-fire antenna can significantly reduce the unaveraged peak SAR (similar to 3 W/kg), 1-g averaged peak SAR (similar to 0.1 W/kg), and power absorption in the head.