In spite of its sufficiently accurate approximation of inherent damping reactions in the analysis of elastic structures, the Rayleigh damping model generates unrealistically large (fictitious) damping reactions when used in the analysis of inelastic structures. One of the popular effective solutions to avoid such fictitious damping reactions is constructing the Rayleigh damping matrix on the basis of tangent (instead of initial) stiffness matrices. This approach, however, leads to two physical inconsistencies, which can adversely affect simulation predictions: (1) instantaneous jumps in damping reactions due to sudden changes in tangent stiffness matrices (e.g. upon yielding or sliding) – which often cause solution algorithm convergence failures; and (2) destabilizing (as opposed to resisting) damping reactions when tangent stiffness matrices turn negative definite (e.g. upon softening) – which generates energy in the system, instead of dissipating it, thereby corrupting response predictions. Considering that Dr. Salehi needed to perform a host of dynamic analyses on softening RC structures and HSR columns (with expected sliding) during his Ph.D. research, he developed an Enhanced Rayleigh damping model to eliminate the above physical inconsistencies of the Rayleigh damping model with tangent stiffness. The Enhanced Rayleigh damping model treats the above problems through, first, replacing the negative eigenvalues of tangent stiffness matrices with zeros, and second, introducing a first-order time differential model into the model, which enforces continuous variation of damping reactions with respect to time. Extensive evaluation of this damping model via dynamic analyses of various systems has shown its effectiveness in tackling the above-mentioned problems.