The author uses a well-known eigenfunction expansion method to solve nonstationary dynamic problems for elastic piezoelectrics. An orthogonality property is established for the eigenfunctions of the mechanical displacement, thus allowing for an expansion of the latter as in the theory of elasticity. The electric potential, however, is expressed as a series in non-orthogonal eigenfunctions, plus a component which is determined from the solution of Laplace's equation for an anisotropic medium. The method is then applied to the problem of instantaneous electrical loading of a piezoceramic rod. A comparison is carried out with the method based on the Fourier transform technique.