A novel finite element (FE) formulation involving external electrical degrees of freedom is proposed for cases dealing with the coupling of mechanical and electrical waveguides through an array of piezoelectric patches. Interconnections between successive periodic unit cells enable the use of the transfer matrix (TM) formalism. It is thus shown that the wave finite element (WFE) method can be applied to electromechanical waveguides. As both mechanical and electrical variables are enclosed in the state vectors, the resulting attenuation and phase constants define waves that propagate in the two domains. For the computation of frequency response functions, it is proposed to employ the Riccati transfer matrix (RTM) method in order to avoid numerical instability. The whole computational method is validated through two examples involving a rod and a beam coupled to passive electrical transmission lines interconnecting a piezoelectric array.