The damping model and its effects on the structural response computed with Nonlinear Response History Analysis (NRHA) requires further investigation, as the physical meaning of the available damping models and their influence on the response are not very clear. This study applies the two most popular damping models, Modal and Rayleigh, to the seismic analysis of a representative six-story Italian reinforced concrete building designed for gravitational loads only. Two structural configurations are considered, with and without masonry infills. NRHAs were performed using 45 pairs of unscaled ground motion records selected for a 475-year return period. The goal is to evaluate the effects of these two damping methods and of the damping values on the building's demand, alongside their practical implications for computational efficiency.