This paper presents the results of a numerical parametric study on the seismic behaviour of 3-D Gaussian-shaped valleys subjected to vertically propagating incident waves. The medium was assumed to have a linear elastic constitutive behaviour. All calculations were executed in the time domain using the direct boundary element method. Representations of the amplification patterns of a valley were developed using both time-domain and frequency-domain responses. It was shown that wavelength and site geometry, including shape and dimension ratios and, to some extent, wave type are the key independent parameters governing valley amplification behaviour. Although 2- and 3-D valleys with similar shape ratios had similar characteristic periods, the 3-D valley had greater maximum deamplification potential and greater relative amplification potential along the valley.