An equivalent, single-layer model for Lamb wave generation by interdigital transducer (IDT) on composite host structures is developed. The additional complexities generally encountered while launching the surface acoustic wave (SAW) on composite structure, such as the coupling between the Lamb wave modes, the complicated nature of the electromechanical actuation etc. are considered. The model of infinite IDT is extended to deal with the finite IDT with edge discontinuities. The effect of electromechanical actuation on the wavelength shifts with respect to the passive case is investigated. The problem of electrically driven instability within the IDT is analyzed. Numerical results are reported by considering a model of the IDT integrated with the host structure, which shows that there are significant deviations from the conventional design estimates while launching a targeted mode. The proposed approach may enable one to obtain new designs in material systems arid geometry that avoid mode-mixing, or to introduce it by choice.