The unsteady surge behavior of a turbocharger compression system is studied computationally by employing a one-dimensional engine simulation code. The system modeled represents a new turbocharger test stand consisting of a compressor inlet duct breathing from ambient, a centrifugal compressor, an exit duct connected to an adjustable-volume plenum, followed by another duct which incorporates a control valve and an orifice flow meter before exhausting to ambient. Characteristics of mild and deep surge are captured as the mass flow rate is reduced below the stability limit, including discrete sound peaks at low frequencies along with their amplitudes in the compressor (downstream) duct and plenum. The predictions are then compared with the experimental results obtained from the cold stand placed in a hemi-anechoic room. The computational results are shown to be capable of reproducing a number of key experimental observations, including the details of low-frequency pressure fluctuations in the compressor ducts and plenum; and the transition from stable operation to oscillating mild surge.