Metamaterials are artificial composite materials engineered to have properties that may not be found in nature.By exploring locally resonant effect of the building units,elastic metamaterials are able to possess negative values of effective mass,effective bulk or shear modulus.Mass-spring and continuum material versions of these elastic metamaterials are reported and the physical mechanisms of negative effective parameters are demonstrated.Applications of metamaterials to acoustic cloaking and superlensing are also discussed.((c) 2012 The Chinese Society of Theoretical and Applied Mechanics.