In the science of physics, elasticity is the ability of a deformable body (e.g., steel, aluminum, rubber, wood, crystals, etc.) to resist a distorting effect and to return to its original size and shape when that influence or force is removed. Solid bodies will deform when satisfying forces are applied to them. Elasticity solution of materials will be grouped in forms of linear and nonlinear elasticity formulations. The main subject of this book is engineering elasticity and consists of five chapters in two main sections. These two main sections are ""General Theorems in Elasticity"" and ""Engineering Applications in Theory of Elasticity."" The first chapter of the first section belongs to the editor and is entitled ""Analytical and Numerical Approaches in Engineering Elasticity."" The second chapter in the first section is entitled ""A General Overview of Stress-Strain Analysis for the Elasticity Equations"" by P. Kumar, M. Mahanty, and A. Chattopadhyay. The first chapter of the second section is entitled ""FEA and Experimental Determination of Applied Elasticity Problems for Fabricating Aspheric Surfaces"" by Dr. D.N. Nguyen. The second chapter is entitled ""Concept of Phase Transition Based on Elastic Systematics"" by Dr. P.S. Nnamchi and Dr. C.S. Obayi. The third chapter is entitled ""Repair Inspection Technique Based on Elastic-Wave Tomography Applied for Deteriorated Concrete Structures"" by Dr. K. Hashimoto, Dr. T. Shiotani, Dr. T. Nishida, and Dr. N. Okude. Finally, this book includes the basic principles of elasticity and related engineering applications about theory and design.