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We analyse cylindrical cloaks designed to control either bending waves, or coupled in-plane pressure and shear waves in elastic plates. Whereas electromagnetic cloaks require symmetric rank 2 tensors of permittivity and permeability, our approach is based upon the introduction of an asymmetric rank 4 tensor of elasticity and a scalar density. For the special case of bending waves in thin plates, the cloak is described by a rank-2 Young tensor and a scalar density, which are both spatially varying coefficients appearing within a transformed fourth-order partial differential equation. These parameters are mimicked by concentric layers of homogeneous materials using averaging techniques. Applications could be in passive anti-earthquake systems.

metamaterials; acoustics