Elasticity is the ability of a material body to return to its original shape and size after the removal of a deforming force. The performance of materials can be defined according to their physical characteristics: stiffness, strength, hardness, ductility, and toughness. The elasticity of materials can be predicted by computational simulations and/or measured in laboratory experiments. This book is divided into two sections: "Simulations and Modeling" and "Characterization". In particular, seven relevant topics and their applications are considered: theory, simulation, characterization, composites, single crystals, nanoindentation, and dielectric elastomers. Examples are provided of the elasticity of materials including composites, single crystals, auxetics, and dielectric elastomers. The book provides important practical skills and will be useful for postgraduate and higher-level science and engineering students.