This chapter presents the basic principles of design, characterization, and applications of elastic metamaterials. Metamaterials are artificial materials engineered to have properties that may not be found in nature. Elastic metamaterials gain unusual properties from their subwavelength microstructures, through local resonances to create negative values of effective mass, effective bulk or shear modulus. Although the content is not able to include all the advances in such interdisciplinary field, it provides readers a comprehensive overview on wave characteristics of elastic metamaterials.