Using the finite element method, the dynamic model of the rotor system with damage of slowly varying mass is proposed. By extending the rotor system with slowly varying mass to the rotor system with generalized inertial damages, the dynamics of the rotor system with slowly varying mass subjected to abrupt phase change are studied. In addition, the dynamics of the rotor system with slowly varying mass subjected to rubbing faults with different rubbing levels are studied by combining the three dimensional orbit. The specific characteristics of the rotor system with rubbing fault while taking the slowly varying mass into consideration are given. The results can be referred to as dynamics of the rotor system with inertial damages and diagnosis of corresponding faults.