The generation of screech tones in an underexpanded jet is investigated by means of compressible large eddy simulation ͑LES͒. A three-dimensional planar geometry is considered with the aim of studying screech radiation in a simple jet configuration, whose physics nevertheless remains similar to that of large-aspect-ratio rectangular jets encountered in experimental surveys. The jet operates at fully expanded Mach number M j = 1.55, with Reynolds number Re h =6ϫ 10 4. The LES strategy is based on explicit selective filtering with spectral-like resolution, and low-dispersion and low-dissipation numerical algorithms are implemented to allow the direct noise computation of the phenomenon. The numerical results are first set against experimental data to establish the consistency of the simulation. It is shown that the flow development and the shock-cell structure are in agreement with experiments of the literature. Furthermore, the upstream acoustic field exhibit harmonic tones that compare correctly to screech tones observed on rectangular jets in terms of frequency, amplitude, and phase shift on either side of the jet. The extrapolation of the LES near-field data to the far field demonstrates that the radiated noise includes the three characteristic noise sources of supersonic shock-containing jets: screech tones, shock-associated noise, and mixing noise, with frequencies and directivities in agreement with experimental observations. Flow visualization of shock/vortex interactions near the third shock-cell finally provides evidences that screech sound sources can be interpreted using the shock-leakage theory. It is shown in particular that the third compression shock within the jet can leak outside through regions of the shear layer with low level of vorticity and results in the production of upstream-propagating sound waves contributing to screech tone radiation.