It has long been recognized that the effects of superficial geological layers, or site effects, can play a major role on the seismic ground motion at the free surface. In this study, we compute wave propagation in a 2-D asymmetrical basin considering both soil non-linearity and pore-pressure effects. Equations of elastodynamics of wave propagation are solved using the spectral element method (SEM). The geometry of the basin gives rise to basin-edge generated waves, that are different for in-plane (P-SV) and out-of-plane (SH) wave propagation and resulting in different non-linear response. Moreover, the excess-pore pressure development in superficial liquefiable layers (effective stress analysis) brings larger deformation and loss of strength than the analysis without pore-pressure effects (total stress analysis). The coupling of vertically propagating waves and the waves specifically generated in 1-D model leads to waves whose amplitude and duration are higher than the 1-D case. This multidimensional effect increases material non-linearity. Such complex wavefield provokes larger deformation and higher pore-pressure rise that cannot be predicted by 1-D modelling. Therefore, our paper suggests the use of multidimensional modelling while studying seismic wave propagation in both linear and non-linear complex media. © The Author(s) 2019. Published by Oxford University Press on behalf of The Royal Astronomical Society.