Electron tunnelling through the Pt(100)\water interface was studied by numerical methods. Molecular dynamics simulation was used to generate equilibrated configurations of the system. Then the potential barrier profiles, experienced by a tunnelling electron, were obtained by calculating the potential energy of the electron due to the surrounding water molecules. Finally the tunnelling probability profile of the electron was computed in one dimension perpendicular to the platinum surface above different adsorption sites. The potential barrier profiles show that tunnelling is highly improbable from a top site and that it is also hindered from a bridge site. At a hollow site, however, the probability of tunnelling through the adsorbed water layer is highly increased; it is only restrained by the second water layer. The potential barrier in the bulk is nearly constant as it is expected for homogeneous dielectrics. The tunnelling probability profiles show that on average there is a steep decrease of the probability next to the Pt(100) surface and that it increases if the tip is 0.2 to 0.3 nm farther away in accordance with experimental observations. This indicates that our calculations give at least a qualitatively correct approximation of the tunnelling barrier. The agreement between theory and experiment also strongly supports the validity of our present picture of the structure of the Pt(100)\water interface.