We study the effect of a superficial layer overlying a half-space on the surface displacements created by a dip-slip dislocation on a planar rectangular fault using a 2-D finite element model. The effect of the density and Poisson’s ratio is negligible. On the other hand, the contrast in Young’s modulus between the top layer and the half-space below significantly affects the modelled coseismic displacements. The horizontal displacements are more sensitive than the vertical displacements to the existence of the top layer. Near the fault, a low-rigidity layer with a Young’s modulus of 10 GPa can increase the horizontal displacements by up to 40 per cent. An analytical 3-D half-space model is used to interpret this effect in terms of an ‘equivalent’ homogeneous model. The presence of a top layer can be partly simulated in a homogeneous half-space by perturbing the depth and the slip on the fault from their ‘real’ values to ‘equivalent’ values. For a given displacement field observed at the surface, the perturbations in fault depth and slip can reach 1 km and 25 per cent respectively. The fault dip angle is not model-dependent. We conclude that for the accurate estimation of fault depth and slip from coseismic geodetic data, rigidity contrasts existing within the upper crust must be taken into account. Not taking into account the effect of an existing low-rigidity layer also leads to an underestimation of seismic moment release. This may in part be the cause of apparent discrepancies between seismic and geodetic moment releases in particular areas such as the Gulf of Corinth, Greece.