In the present study, a new model-based method for rotor crack detection and crack location is proposed. The finite-element model of the rotor-bearing system accounts for the breathing mechanism of the crack. The model of the rotor system is augmented with an auxiliary single-degree-of-freedom oscillator. The observer is designed and the estimates of its two auxiliary state variables are proposed as crack indicators. The crack location along the shaft is determined by designing a set of observers, which calculate the values of these indicators for different possible crack locations along the shaft. The proposed method is validated numerically and the results prove its capability to detect and locate the crack. Further study will include experimental and numerical investigations to make the approach more robust.