The problem of the reflection of elastic stress pulses at the interface between a rod and a half‐space is treated theoretically and experimentally. The axis of the rod is taken to be perpendicular to the free surface of the half‐space and its flat end to be in frictionless contact with this surface. It is shown that for the reflection of an infinite train of sinusoidal waves at such a boundary the conditions are analogous to those that apply for the reflection of such a train at the boundary between an elastic and a linear viscoelastic rod, and that a “cross‐over effect” may be observed. This effect is that a critical frequency ωcmay exist such that if the frequency of the incident wave is ω the phase of the reflected wave shows a sudden jump of π as ω passes through ωc. Thus if a dc pulse is reflected at the interface and if its relevant Fourier spectrum extends over this critical frequency, an s shaped pulse is found to be reflected. It is also shown in this paper that the accuracy with which the dynamic properties of the material of the haft‐space can be determined is limited by the precision with which the values of the Fourier components of the incident and reflected pulses are known.