Using the discrete wave number representation method (Bouchon and Aki, 1977; Bouchon, 1979), we model the Parkfield earthquake of 1966 as a Haskell-type dislocation source embedded in a layered medium. We show that the displacement and velocity recorded near the source (station 2 of the Cholame-Shandon array) can be fully accounted for by the propagation of the rupture on the branch of the fault closest to the station. The slip and slip velocity inferred are about 40 cm and 130 cm/s, respectively. The ground motion at the accelerograph site and in the region close to the source was very strongly amplifield by the sedimentary layer. The rupture, after being initiated at depth, stayed buried well under the sediments on the main segment of the fault. The dislocation then jumped across Cholame Valley and became quite shallow. On this southeast branch of the fault the rupture most likely penetrated the sediments. The results obtained constitute an encouraging step toward predicting the strong ground motion at a given site for a potential earthquake fault.