In conducting experiments on waves in an elastic rod, J. Oliver discovered a new mode of symmetric vibration in which the motion was predominantly at the end of the rod. It is shown that this “end mode” arises when pure extensional waves are coupled with waves with complex wave numbers. Approximate equations are used to study the reflection of pure extensional waves at the end of a semi‐infinite rod. The properties of the resulting end mode are studied in detail and are compared with the phenomena reported by Oliver.