Pedestal looseness and supporting stiffness nonlinearities usually occur in rotating machines. To enhance the robustness and accurately forecast the nonlinear behaviors of rotor systems, these two kinds of common nonlinearities should be considered so that to meet the requirements of the dynamical design of a multi-disk rotor system. In this paper, the rotor system model with cubic supporting stiffness and looseness fault is established by the Lagrange method. The harmonic balance (HB) and Runge–Kutta (RK) methods are used to solve the dynamic response of the double disk rotor system, and the accuracy of the HB method is justified in comparison to the RK method. The bifurcation diagram, time history, frequency spectrum, phase portrait and Poincaré map are provided to discuss the individual and coupling effects of these two nonlinearities on the transient and steady-state response. The obtained experimental results indicate that the proposed model can capture the main nonlinear behaviors of looseness fault and nonlinear supporting stiffness, verifying the accuracy of theoretical and numerical results.