Studies have shown that random vibration theory (RVT) site‐response analysis predicts site amplification at the natural site frequencies that are systematically larger than the results obtained from time series (TS) analysis using a suite of input TS. A critical part of the RVT approach is the peak factor, defined as the ratio of the peak to root mean square (rms) value of a signal. This study investigates the influence of different peak factor models on the site amplification estimated by RVT site‐response analysis. It is shown that the use of the Vanmarcke (1975) peak factor model rather than the Cartwright and Longuet‐Higgins (1956) peak factor model predicts site amplification in better agreement with those predicted by TS analysis, although some differences remain for some cases. Larger differences between the RVT and TS results occur for sites with smaller natural frequencies, for earthquakes of smaller magnitude, and for sites with larger bedrock shear‐wave velocities. Accounting for the increase in duration due to site response in the RVT analysis minimizes the differences between RVT and TS analysis. Recommendations are provided regarding the cases where RVT provides site amplification reasonably similar to TS analysis.