This work presents a statistical study on the effect of soil layers with uncertain properties on ground-motion intensity at the soil surface. Surface motion is obtained by applying multiple real rock earthquake records at the base of different characterizations of the soil column, each one generated via Monte Carlo simulation. The effect of the soil is studied in terms of a site-specific, frequency-dependent amplification function, af(f), where f is a generic oscillator frequency. The goal here is the identification of ground-motion parameters that allow an efficient prediction of af(f). We investigated magnitude, M, source-to-site distance, R, of the input bedrock accelerogram along with bedrock ground-motion parameters such as peak ground acceleration, pgar, and spectral acceleration values, and , both at the generic frequency f and at the specific initial fundamental frequency of vibration, fsc of the soil column. This work includes two case studies: a saturated sandy site and a saturated soft clayey site. In the former, loss of shear strength owing to cyclic mobility is anticipated for severe levels of ground shaking, while in the latter, significant amplification is expected at long oscillator periods. The results show that of the input record is the single most helpful parameter for the prediction of af(f) at the same oscillator frequency, f. is more informative than pgar and/or the pair of M and R values of the event that generated the bedrock motion. A sufficiently accurate estimate of the median af(f) can be obtained by using 10 or fewer records, which may be selected without undue attention to the specific scenario events (i.e., M and R pairs) that control the hazard at the site. Finally, the effect of the uncertainty in the soil parameters on the prediction error of af(f) is of secondary importance compared to that from record-to-record variability. These findings will be used to estimate the hazard at the soil surface in a companion article in this issue (Bazzurro and Cornell, 2004).