The effect of topography on ground motion has been well recognized during numerous earthquakes. Several studies present observational evidence from destructive earthquakes, where the damage is higher in the vicinity of hills and near slope crests. Furthermore, a number of numerical studies aimed to reproduce this phenomenon using different numerical methods, e.g. Finite Elements, Finite Differences and Boundary Elements have been carried out. Most of these investigations involve parametric studies, considering different variables. However, one of the assumptions of these studies is a homogeneous soil stiffness with depth, which is not in most cases realistic. This article investigates the effects of canyon topography on ground motion considering different soil stiffness profiles over a rigid bedrock. Three soil profiles with stiffness variation with depth are examined and compared to the case of a soil layer of uniform stiffness. An additional analysis of a two- layer medium lying above half-space is also considered. Time domain numerical analyses are carried out with the Imperial College Finite Element Program ICFEP, considering linear elastic soil behaviour over rigid bedrock. The input motions are wavelets of harmonic nature, modified by a Saragoni and Hart (1973) temporal filter. These wavelets with a characteristic. pulse period Tp in the range of 0.1 s to 2 s are analysed. This study confirms that the topographic amplification extrema are located between the natural periods of the corresponding one-dimensional free-field profile in agreement with recent previous studies. Furthermore, the amplitude of the topographic amplification peaks is shown to change for the different examined soil stiffness profiles.