To understand pipe failures due to water hammer, the dynamics of generalized stresses first require consideration. Elastic stresses are the focus of this dynamic analysis, even though dynamic plastic stresses are briefly treated in this text. The fact is that plastic deformation dynamics is far from being fully understood. Even elastic structural dynamics needs much work. In short, suddenly applied loads induce shock waves, which in turn cause vibrations and dynamic strains, where these strains are related to dynamic failure stresses through material properties.