The equivalent viscous damping is a key parameter in the prediction of the maximum nonlinear response. Damping constitutes a major source of uncertainty in dynamic analysis. This paper studies the effect of using viscous damping, on the reduction of the seismic responses of reinforced concrete RC frame buildings modeled as three-dimensional multi degree of freedom (MDOF) systems, and the use of nonlinear time history analysis as a method of visualized behavior of buildings in the elastic and inelastic range. This study focuses on the implications of the available modeling options on analysis. This article illustrates the effect of using the initial or tangent stiffness in Rayleigh damping in analysis of structures. Correspondingly, this work is also concerned with the estimation of Rayleigh, mass-proportional or stiffness-proportional damping on engineering demand parameters (EDPs). As a result of a series of considerations, a damping modeling solution for nonlinear time history analysis (NLTHA) was carried out to compute the damage index. The application example is a building designed according to reinforced concrete code BAEL 91 and Algerian seismic code RPA 99/Version 2003 under seven earthquake excitations. The simulations demonstrated the accuracy and effectiveness of the proposed method to account for all of the above effects.