This work, in two parts, proposes, in this first part, an electromechanically coupled finite element model to handle active-passive damped multilayer sandwich beams, consisting of a viscoelastic core sandwiched between layered piezoelectric faces. The latter are modelled using the classical laminate theory, whereas the face/core/face system is modelled using classical three-layers sandwich theory, assuming Euler-Bernoulli thin faces and a Timoshenko relatively thick core. The frequency-dependence of the viscoelastic material is handled through the anelastic displacement fields (ADF) model. To make the control system feasible, a modal reduction is applied to the resulting ADF augmented system. Validation of the approach developed in this part is presented in Part 2 of the paper together with the hybrid damping performance analysis of a cantilever beam. Copyright