This paper investigates the effect of inherent damping modeling on the computed seismic response and collapse performance of selected seismically isolated buildings. The analyzed seismically isolated buildings were designed by the procedures of the ASCE/SEI 7-16 standard. The structure is a six-story perimeter frame building designed with special moment resisting frames or with special concentrically braced frames (SCBF) for a location in California. Three different seismic isolation systems are considered: (i) triple friction pendulum (TFP) bearings without moat walls, (ii) TFP bearings with moat walls (double concave [DC] friction pendulum bearings with moat walls have effectively the same ultimate behavior), and (iii) DC friction pendulum bearings without moat wall.The superstructure inherent damping schemes considered are (i) zero damping, (ii) modal damping, (iii) Zareian-Medina damping, (iv) added virtual viscous dampers with and without force-caps, and (v) added virtual viscous dampers with the same damping constant value. The response parameters computed are peak floor accelerations, peak story drift ratios, peak residual story drift ratios, peak isolator horizontal displacement, and floor acceleration spectra. Also, the probability of collapse in the maximum considered earthquake (MCE R ) is computed. It is shown that the modeling approach for the inherent damping has minor effects on the computed responses and the collapse probability of the studied seismically isolated buildings, except for the peak floor acceleration and the floor response spectra for periods below one second. It is suggested that a convenient way to model inherent damping is to use virtual viscous dampers with all having the same damping constant.