A two-dimensional elastic finite-element method is used to investigate the weak-motion seismic response of the Aburra Valley of Medellin, Colombia. A vertically propagating anti- plane SH Ricker wavelet is used to study the response of the valley for frequencies up to 5 Hz. The Aburra Valley is very large and geologically diverse. The -1200-metre-deep and -15- kilometre-wide valley is covered by a variable layer of soft soils averaging some 30 metres deep. The soils are mainly residual, alluvial or debris-flow deposits. The valley also contains a network of 24 strong-motion seismic recorders. A 49,900-element mesh of a cross-sectional model through the southern end of Medellin is analysed using the finite-element software package, Archimedes. The results are presented in both time and frequency domains. A similar one-dimensional finite-element method is used for comparison. It is found that while amplification often occurs at frequencies defined by a one-dimensional analysis, the level of amplification is often highly dependent on multi-dimensional effects. Local irregularities in the stratigraphy and topography at some sites have a significant effect on the seismic response. Site response may also be influenced strongly by sub-valley structures up to a few kilometres across, yet the influence of the valley as a whole is small. Poor correlation between modelling results and recorded data is probably due to a lack of site-specific detail within the model, and the limiting two-dimensional nature of the analysis.