The present investigation is concerned with the wave propagation of generalized thermoelastic diffusion on a half space with energy dissipation. The surface of the half-space is taken to be traction free and a thermal shock applied on the surface. The problem has been solved numerically using a finite element method. The expressions for displacement components, stresses, temperature, concentration and chemical potential so obtained in the physical domain are computed numerically and illustrated graphically at different times. Comparisons are made with the presence and absence of diffusion.