A wave theory method is used to determine the effect of a sinking lithospheric slab on short-period and long-period waves. We consider a simplified model of the lithospheric slab with a 10 per cent velocity contrast and compute both short-period and long-period theoretical seismograms from a P-wave source located in or near the slab. For this model, the ray-theoretical amplitude agrees quite well with the short-period amplitude. In the ray-theoretical shadow zone the long-period seismograms (15- to 25-sec dominant period) typically have amplitudes 50 per cent (or greater) of the direct P-wave amplitude and exhibit wave-form broadening. Similar wave-form broadening has been attributed to the dynamics of earthquake faulting. The effect of the lithosphere on long-period waves from nearby sources must be taken into account in studies which utilize the observed variation in wave-form broadening to infer earthquake source dynamics.