This textbook aimed at upper-level undergraduate and graduate engineering students who need to describe the large deformation of elastic materials like soft plastics, rubber, and biological materials. The classical approaches to finite deformations of elastic materials describe a dozen or more measures of stress and strain. These classical approaches require an in-depth knowledge of tensor analysis and provide little instruction as to how to relate the derived equations to the materials to be described. This text, by contrast, introduces only one strain measure and one stress measure. No tensor analysis is required. The theory is applied by showing how to measure material properties and to perform computer simulations for both isotropic and anisotropic materials. The theory can be covered in one chapter for students familiar with Euler-Lagrange techniques, but is also introduced more slowly in several chapters for students not familiar with these techniques. The connection to linear elasticity is provided along with a comparison of this approach to classical elasticity.