Book excerpt: The analytical aspects and developments in the concepts of computational stability are discussed in this book. Stability is the primary concern in both design and evaluation of load-carrying systems and is a major issue in the area of engineering science and mechanics. Structural instability may cause catastrophic failure of engineering structures; hence, stability requirements must be fulfilled. Comprehension of this topic is highly significant in the fields of civil, mechanical and aerospace engineering. This book discusses the state-of-the-art in stability analysis and compiles several researches demonstrating the developments in this area. It also comprises of original and innovative research studies showcasing different investigation directions and angles.