Intershaft bearing is widely adopted in dual rotor turbofan aircraft engines. Since this kind of dual rotor system has two different rotor speeds and the intershaft bearing leads to the coupling between HP rotor and LP rotor, the calculation of the critical speeds is much more complicated than that of the rotor systems without intershaft bearing. Compared to a single rotor system, the dual rotor system has more critical speeds which can be classified as critical speeds excited by HP rotor and that by LP rotor. In the paper, a finite element rotor model of a high-bypass turbofan jet engine with intershaft bearing is established for the study of critical speeds analysis. The general axisymmetric element is used to model the shafts and disks, and the blades are simplified to mass points. The main bearings including the intershaft bearing are set up with spring element. Assuming that the rotational speed ratio of the two rotors for the dual rotor system is a fixed number, the critical speeds are calculated using three methods based on the finite element rotor model. For the first method, the system critical speeds are obtained directly by Campbell diagram based on QR damped solution method. Then the synchronous unbalance response analyses are carried out and the rotor critical speeds are derived from the amplitude-frequency curves. For the last method, multiple group Campbell diagram analyses are conducted. With one rotor speed fixed at constant rpm N, we can change the speed of the other rotor to obtain one group of critical speeds. By varying speed N of the two rotors, a critical speeds data set can be obtained and plotted as a dual rotor critical speed map. The critical speeds can be easily extracted from the critical speed map according to the rotational speed curve of the engine. The study shows that the dual rotor system critical speeds calculated from above three methods are identical. For the first two methods, the rotational speed ratio of two rotors must be a known and fixed number, which is impossible in reality. The third proposal has no rotation speed relation restriction for rotors, and therefore is recommended for analyzing the critical speeds of aircraft engines with intershaft bearing.