Abstract Rotating stall of multistage centrifugal compressors has always been a topic of great interest for many reasons, but there is no extensive literature on the subject. In this scenario, time-accurate computational fluid dynamic (CFD) approaches can be useful to better understand this phenomenon and push our knowledge forward. In this paper, a 3D-unsteady CFD approach was applied to the simulation of the last three stages of an industrial centrifugal compressor machine to study the unsteady flow patterns induced by rotating stall when moving toward low mass flow. The computational framework is aimed at reproducing repeating-stage flow conditions for the stages consisting of a low-flow coefficient and low-Mach number impeller, a vaneless diffuser, and a return channel. The numerical setup was validated on a single-stage test case with similar design intent, for which unique experimental measurements were available to assess the performance of each component when operated in proximity of the left margin. The signals of dynamic pressure probes recorded at the inlet and outlet of the vaneless diffuser are compared to monitor subsynchronous harmonics related to the rotating stall phenomenon. Numerical and experimental results were found to be in good agreement in terms of integral performance parameters, rotating stall frequency, and amplitude of the unsteady pressure field. This confirms the possibility of exploiting the CFD for the prediction of the complex unsteady flow pattern occurring beyond the left margin of the operating curve.