This paper describes simulations of the flow development and noise radiation of a circular and a square jet. The three-dimensional Navier-Stokes are solved using the Detached Eddy Simulation as the turbulence model. The jet nozzles are included in the calculations. To simulate the excitation of the jet plume by the unsteadiness upstream of the jet exit a random excitation is implemented just downstream of the nozzle exit. The predicted mean flow Held development is compared with experimental measurements and good agreement is obtained. The radiated noise is calculated using the permeable surface Ffowcs Williams-Hawkings wave extrapolation method. Predictions of the noise spectra for different observer angles and the overall sound pressure level directivity are made. The predictions show good agreement with the experimental data. The radiated noise characteristics are shown to be similar for the two jet geometries.