The circular piston sound radiation has wide applications. Most of the sound sources for the ultrasonic detection can be considered as the piston radiators. The relationship among the distribution and space position of the propagation wave and evanescent wave on the axis of sound field, the sound source radius and the radiation frequency is analyzed by the angular spectrum method. The effective propagation distance of the evanescent wave is determined by comparing the sound pressure amplitudes of two kinds of waves. The near field acoustic holography (NAH) theory is used to calculate the sound pressure distribution of the evanescent wave in the near field space of the transducer, and the error analysis is also carried out. The simulation results show that both the angular spectrum method and the NAH method based on the spatial Fourier transform can accurately reflect the distribution law that the near field sound pressure of the circular piston radiation is presented exponential decay.