We discuss the application of virtual elements to linear elasticity problems, for both the compressible and the nearly incompressible case. Virtual elements are very close to mimetic finite differences (see, for linear elasticity, [L. Beirão da Veiga, M2AN Math. Model. Numer. Anal., 44 (2010), pp. 231-250]) and in particular to higher order mimetic finite differences. As such, they share the good features of being able to represent in an exact way certain physical properties (conservation, incompressibility, etc.) and of being applicable in very general geometries. The advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity.