For several decades, random vibration theory (RVT) has been a popular method for predicting peak ground motions for seismic hazard assessment. Modern usage of RVT is typically in the stochastic method of simulating peak ground motion, to convert empirical models of the earthquake Fourier amplitude spectrum to response spectra, and in site response analysis. This study reexamines the underlying assumptions of RVT analysis, particularly regarding durations, peak factors, and nonstationarity corrections. It is suggested that the significant oscillator duration is the most appropriate duration metric for predicting response spectra, and an empirical model is derived using New Zealand data. This allows RVT to be easily generalized to levels of oscillator damping other than the usual 5%. For short‐duration excitations, signal nonstationarity is accounted for using a theoretical time‐dependent power spectral density function. This allows proper consideration of nonstationarity in both the signal standard deviation and the signal bandwidth. The appropriateness of commonly used Gaussian‐process peak factors is also examined. It is shown that low‐frequency oscillator response signals are not well approximated by a Gaussian distribution, which causes low‐frequency response spectra to be overpredicted. This means RVT‐optimized duration models in the literature do not have a physical interpretation at low oscillator frequencies. RVT analysis only yields approximate results, with standard deviations of 0.25 natural log units. However, it is nevertheless a simple and convenient method for rapidly predicting peak high‐frequency ground motions.