The dynamic fundamental solution for fully anisotropic Kirchhoffs plates is derived here. The solution is obtained using a key proposition for quasi-hyperbolic operators and a known Laplace transform. The final expression is given as an one-dimensional integral over a combination of a rational function and square powers of the two Fresnel Integrals. Additionally, two new integral identities are derived here as a consequence of the uniqueness of the fundamental solution. The solution has been numerically evaluated for three different examples. The numerical results showed agreement with examples of known solutions for the special cases of isotropic and orthotropic media. A fully anisotropic, multi-layer ply composite plate has been analysed using the new solution. Moreover, the dynamic BEM formulation for Kirchhoffs plates is presented here as well, along with the asymptotic behaviour of the time-space singularities of the isotropic solution. Finally, the numerical treatment of a time-space singular integral over a constant boundary element is presented herein. (C) 2015 Elsevier Ltd. All rights reserved.54 1927