The author proves existence and uniqueness of weak solutions to a hyperbolic-elliptic system of PDEs, whichs models forced oscillations in a piezoelectric viscoelastic body. The system consists of a linear dissipative second order hyperbolic system (for the elastic displacement) and a linear second-order elliptic equation (for the electric potential), complemented by boundary conditions (in space) and periodicity conditions (in time), and is formulated on a bounded \(C^2\)-domain in \(\mathbb{R}^3\). For the proof Galerkin's method and corresponding a priori estimates are used.