Use is made of second-order elasticity theory to derive an estimate of the change in travel time with stress for compressional waves which propagate along the principal stress directions in a homogeneous layer of material. A particular stress system is chosen which can be expected to produce a strike-slip fault. Laboratory data for Barre, Vt. granite, interpolated for a depth of approximately 1 km, are used to obtain a numerical result. The change in travel time is found to be 0.075 milliseconds per km per bar. Since timing precision of better than ±1 millisecond can be achieved for refraction paths up to some 40 km in length, it is concluded that stress changes of several bars are within the range of detectability in carefully executed field experiments.