Aeroacoustic mechanisms of an axisymmetric over-expanded supersonic jet impinging on a flat plate with and without hole are numerically investigated. High-order weighted compact nonlinear scheme is used to simulate the unsteady flow including shock waves and sound radiation in the near field of the jet. Analyses of unsteady flowfield and related near-sound field reasonably identify three major noise generation mechanisms, that is, noises from Mach wave, shock cell-shear layer interaction and small fluctuations of jet shear layer. Especially, intense noise radiation in the form of Mach waves and its reflection at the plate predominates the noises from the other two finer sources. The simulated distributions of sound source power and its frequency along the jet axis qualitatively well coincide with typical experimental data used in NASA SP-8072. Similar sound pressure spectrum shape is obtained both the cases of flat plate with and without hole, but the case of without hole shows higher SPL by several dB than that of with hole due to the stronger Mach wave radiation. Aeroacoustic flowfield is drastically affected by the Reynolds number because the jet shear layer instability directly causes the strength of acoustic waves.