  The paper addresses an important issue of cloaking transformations for
fourth-order partial differential equations representing flexural waves in thin
elastic plates. It is shown that, in contrast with the Helmholtz equation, the
general form of the partial differential equation is not invariant with respect
to the cloaking transformation. The significant result of this paper is the
analysis of the transformed equation and its interpretation in the framework of
the linear theory of pre-stressed plates. The paper provides a formal framework
for transformation elastodynamics as applied to elastic plates. Furthermore, an
algorithm is proposed for designing a square cloak for flexural waves, which
employs a regularised push-out transformation. Illustrative numerical examples
show high accuracy and efficiency of the proposed cloaking algorithm. In
particular, a physical configuration involving a perturbation of an
interference pattern generated by two coherent sources is presented. It is
demonstrated that the perturbation produced by a cloaked defect is negligibly
small even for such a delicate interference pattern.
