In this study, nonlinear disturbance equations are solved in two and three dimensions to investigate the sound generated by compressible plane mixing layers. Two flow regimes are distinguished : coflow and counterflow mixing layers. The simulations of coflow shear layers has been carried out in two- and threedimensions. In both cases, the main radiation is attributed to the pairing events leading to a quadrupolar signature. The convective nature of the flow is conform with the linear stability calculations. On the contrary, the two-dimensional simulation of a counterflow mixing layer illustrates a typical oscillator behaviour of the flow.