Aerodynamic instabilities such as stall and surge may lead to mechanical failures. They can be avoided by better understanding and accurate prediction of the associated flow phenomena. Numerical simulations of rotating stall do not often match well the experiments as the number of cells and/or their rotational speed are not correctly predicted. The volumes surrounding the compressor have known effects on rotating stall flow patterns; therefore, an increased need for more realistic simulations has emerged. In that context, this paper addresses a comparison of numerical stall simulation in a compressor alone with a numerical stall simulation including the additional compressor rig. This study investigates the influence of the upstream and downstream volumes of the compressor rig on the rotating stall flow patterns and the consequences on surge inception in a high-pressure, high-speed research compressor. The numerical simulations were conducted using an implicit, time-accurate, 3D compressible Reynolds-averaged Navier–Stokes (URANS) solver. First, rotating stall is simulated in both configurations, and then the outlet nozzles are further closed to bring the compressors to surge. The numerical results show that when the compressor rig is accounted for, fewer cells develop in the third stage and their rotational speed is slightly higher. The major difference linked to the presence of the rig lays in the existence of a 1D low frequency oscillation of the static pressure, which affects the entire flow and modifies surge inception. The analysis of the results leads to a calculation of the thermo-acoustic modes in the whole configuration, which shows that this low frequency corresponds to the third thermo-acoustic mode of the complete test-rig.