The pulse velocity method is the most widely used ultrasonic nondestructive method for assessing concrete quality. However, it has been well established that the relation between ultrasonic pulse velocity and concrete strength is, in general, not reliable enough for practical purposes; nevertheless, essentially the same method has been used for over 40 years. This paper is a critical analysis of the existing ultrasonic pulse velocity method as well as an attempt to explain it's failure for strength determination and damage detection in concrete. First, the theory and technique of the ultrasonic pulse velocity method is introduced. Next, misconceptions concerning the relation between pulse propagation parameters and concrete strength are clarified. In addition, original experimental data are presented that demonstrate the insensitivity of the ultrasonic pulse velocity method to the present strength of a variety of materials including concretes, mortars, and pastes. The end result of this study is a better understanding the ultrasonic pulse velocity method - as applied to concrete - as well as a better understanding of the limitations of this technique.