Abstract: This paper studies the damping problems in damage based structure FEM modeling. Damping damage is proposed to formulize the damping variation when damages occurr. The accompanying damping damage and the original damping damage are defined. Several damage modeling methods are investigated to evaluate its performance in damping damage modeling. Comparison of these methods is given by numerical studies. Moreover, the effect of local stiffness damages upon the local damping properties, vibration energy distribution, and the behaviors of damp dissipation of structures are investigated separately. It is suggested that the stiffness damage and damping damage should be considered simultaneously in structural damage modeling, and the suitable damage modeling methods should be chosen.