A theoretical model, based on mode theory, is presented in order to study the behavior of the Stoneley wave when it reaches the extremity of a thick plate immersed in a liquid. The superposition of two phenomena is established: the first one being the simple forward diffraction of the Stoneley wave in the liquid and the second one being its conversion into two generalized Rayleigh waves which propagate on the same plane as the incident Stoneley wave or along the vertical end face of the solid support. The theoretical analysis is in good agreement with the experimental observations of Tinel [Ph.D. Thesis, Université Le Havre, France (1991)].