In some tensile tests with brittle materials, it was noted that fractures were produced at two different cross sections of the specimen when the rupture load was reached. The phenomenon of the second fracture prompted the present investigation. It is believed that the second fracture is caused by the destructive action of the elastic strain waves created during the first of the two fractures. The analytical and experimental work carried out was focused on describing the character of these waves. Consideration of the mechanics involved reduces the problem to that of a vibrating cantilever beam with time-dependent boundary conditions. Two types of waves are shown to exist. The first is a longitudinal unloading wave (compression). The other is a group of flexural strain waves caused by the moment that develops at the initial fracture section. The methods of operational mathematics and the electric-analog computer have been employed in the analytical study.