The addition of viscoelastic braces in structures for vibration reduction has been proposed and implemented in the past decade in metal scaled models of full-scale structures. Viscoelastic braces can provide energy dissipation, while the structure remains elastic. In reinforced concrete structures, the seismic response is usually inelastic, which is often accompanied by permanent deformations and damage. The addition of viscoelastic dampers can dissipate energy at the early stages of cracking of the concrete elements and reduce the development of damage. With proper selection of dampers, this damage can be substantially reduced or even eliminated. However the addition of viscoelastic dampers may stiffen the structure unnecessarily producing increased inertial forces and base shears when subjected to seismic motion. The quantification of the influence of viscous damping and elastic stiffness properties of dampers during the inelastic response of reinforced concrete structures is the subject of this investigation. Models for analysis of inelastic response with damage indexing for reinforced concrete structures that include viscoelastic braces are developed and calibrated using experimental data produced by shaking table tests. These models are then used to determine the variation of expected damage in the presence of damping and quantify the hysteretic energy dissipation along with the damping energy.