In this paper, we propose tag antennas and reader antennas, which are suitable for radio frequency identification system. Antennas operating in the ISM and the UHF bands are designed. The antenna dimensions are minimized by employing the meander-line technology. Adopting the concepts of Yagi-Uda antennas, We use parasites to increase the antenna gain and to create an end-fire radiation pattern. The fact that the design comes without a ground plane can achieve cost down of the antenna. Higher antenna gains allow a greater effective read-zone distance. Also, the directional radiation pattern eliminates the degradation of performance due to multi-path loss. The design of tag antennas shows good performances in terms of both cost and antenna characteristics for radio frequency identification systems. The reader antennas are designed. Etching a slit in a square patch can achieve the requirement of circular polarization. It can effectively reduce the polarization mismatch when the tags are point to different orientation. Therefore the reliability of system operation will be improved. The antenna performance is measured by the experiments. Moreover, it will be compared with the simulation. In the latter part of paper, the simulation of the power coupling will be carried out. According to the result of power coupling simulation, we analyze and discuss which factor will affect the reliability of the identification. Identification failure will be effectively avoided and a robust identification system can be built if the analyses are properly employed.