The stability of structures plays a paramount rule in analysis and design of structures. The theory of elastic stability is a subject of interest in Civil, Mechanical and Aerospace Engineering. The instability in most of the times is equivalent to failure. As a result prediction of instability of structures under severe loading conditions in their effective life should be done. Most of the classical books are in static stability theory. The stability under non-conservative force can't be treated with this theory. The dynamic stability is the sole solution. That was the reason for writing this book. The aim of the book is to introduce the principles of the dynamic stability and its application in a concise, simple an accurate manner. The audiences for the book are the post graduate students and researchers in Civil, Mechanical and Aerospace engineering.