Dual-mode Lamb-wave resonator has become a powerful component for clock reference and sensing applications, enabling efficient compensations of temperature effects, concurrent measurements of multiple environmental parameters, etc. An equivalent circuit model for the dual-mode Lamb-wave resonator is indispensable as it provides a means as well as being an effective tool for evaluating device characteristics and to aid the designing of circuitry for the resonators. This could be the first time ever that an efficient equivalent-circuit model, i.e., modified π-type Butterworth-Van Dyke model for dual-mode Lamb-wave resonators is reported. Evaluated by experiments, this model attains noteworthy agreements on both the magnitudes and phases of Y11 and Y21 of the measurement results. Compared to literature, the proposed model is capable of modeling the dual resonances efficiently. Moreover, this work also proves more accurate when viewing the Y-parameters across a wide frequency range. The gained features of this model are most beneficial for the analysis of the dual-mode Lamb-wave resonator and also for the designing of circuits.