Despite great advances on jet screech research during the past few decades, the prediction of jet screech amplitudes still remains a challenging task. The main objective of this paper is to develop an accurate three dimensional computational aeroacoustic procedure for the simulation of screech phenomenon from an underexpanded supersonic circular jet. The three dimensional Navier–Stokes equations and a modified two equation standard kturbulence model are solved in the generalized curvilinear coordinate system. A dispersion-relation preserving scheme is utilized for space discretization. The 2N storage low-dissipation and low-dispersion Runge–Kutta scheme is applied for time marching. Numerical results are presented and compared with available experimental data over Mach number range from 1.17 to 1.60. The predicted shock cell structure and radial density profiles agree very well with the measured results by Panda and Seasholtz ["Measurement of shock structure and shock vortex interaction in underexpanded jets using Rayleigh scattering," Phys. Fluids 11, 3761 (1999)]. In particular, it is shown that not only the predicted wavelengths, but also the amplitudes of the flapping and helical modes are in good agreement with experimental data by Ponton et al. ["Near field pressure fluctuations in the exit plane of a choked axisymmetric nozzle," NASA Tech. Memo TM-113137, 1997]. It is found that although the instantaneous flow fields accompanying the flapping and helical jet screech tones are not axisymmetric yet, the long time average mean flow field is still almost axisymmetric. This is because of the slow rotation of the flapping plane around the jet axis. The real time pressure signal of a Maj=1.30 screeching jet at r /D=2 in the nozzle exit plane is analyzed. The results indicate that the acoustic field of the simulated flapping and rotating motions of the screeching jet agree well with Ponton and Seiner's experimental measurements ["Acoustic study of B helical mode for choked axisymmetric nozzle," AIAA J. 33, 413 (1995)]. © 2008 American Institute of Physics. [DOI: 10.1063/1.2844474]