In this investigation we solve the problem of propagation of a compressional pulse in a solid half‐space which is overlain by a solid layer of different properties. The point source is situated at the depth ½H,Hdenoting the thickness of the layer. Theoretical seismograms of the vertical displacementwat the surface are evaluated out to rangesr= 20H. The solution is obtained by the exact ray theory. The displacementWodue to the source was assumed to have a shape which at large distances reduces to a sawtooth. The once‐reflected waves from the interface,PPandPS, are strongly marked. The Rayleigh wave is already recognizable atr= 5Hand is fully developed atr= 20H. The method of ‘ray theory’ was applied here far into the region where the normal mode theory converges well. The theoretical seismograms are illustrated. The properties assumed for the layer (1) and for the half‐space (2) are λ1= μ1μ2= 2μ1cs2≡c2= 1.1cs1≡