Aerodynamic instabilities such as stall and surge may occur in compressors, possibly leading to mechanical failures so their avoidance is crucial. A better understanding of those phenomena and an accurate prediction are necessary to improve both the performance and the safety. A surge event in a compressor threatens the mechanical integrity of the aircraft engine, and this remains true for a research compressor on a test rig. As a result, few experimental data on surge are available. Moreover, there are technological, restrictive constraints that exist on test rigs and limit severely the type of data obtainable experimentally. This partially explains why numerical simulation has become a usual, complementary and convenient tool to collect data in a compressor, as it does not disturb the flow nor does it encounter technological limits. Despite the inherent difficulties, an entire surge cycle has been simulated in a high-speed, high-pressure, multistage research compressor, using an implicit, time-accurate, 3D compressible unsteady Reynolds-averaged Navier–Stokes solver. First, the paper presents the main features of the surge cycle obtained, along with those from the experimental cycle, for a validation purpose. Four phases compose the surge cycle: surge inception, the reversed-flow phase, the recovery phase, and the repressurization of the compressor flow. All of them are described, and focus is put on surge inception and the reversed-flow phase, as they induce greater risk for the mechanical integrity of the machine.