Abstract: The flow of the supersonic jets contains shock waves, vortices, turbulence and acoustic waves. The numerical simulation method and the mechanism of the shock associated noise of the supersonic jets have been topics of general interest. This paper contains two parts. Firstly, we briefly review the numerical studies on the fundamental problems of the shock associated noise of the supersonic jets. It includes the numerical methods for the shock associated noise, and the models of the supersonic jets, the axisymmetric and three dimensional supersonic jets. For the numerical method, we introduce the technique to reduce the non-physical oscillation and a criterion to design the smoothness indicator for high order shock capturing schemes. Secondly, we introduce our recent results based on the direct numerical simulations and experi-mental verification, including the localization of the axisymmetric modes, the development of trapped waves and the evolution of the flapping modes.