Piezoelectric MEMS speakers are emerging as very promising implementations of loudspeakers at the microscale, as they are able to meet the ever-increasing requirements for modern audio devices to become smaller, lighter and more power efficient [1, 2]. However, research work is still needed to accurately capture their mechanical and acoustical response [3]. In this work, we propose a lumped-parameters equivalent circuit for a fast and accurate modeling of this type of devices. The electro-mechanical parameters are derived from a FEM eigenfrequency analysis, for a precise computation of these quantities for arbitrarily complex geometries and an accurate estimation of the shift of the speaker resonance frequency due to an initial non null pre-deflected configuration. The acoustical parameters are instead derived through analytical formulas. Special attention is paid to the air-gaps modeling, by taking into account the acoustic short-circuit between the speaker front and rear sides. The very good matching in terms of Sound Pressure Level among the equivalent circuit predictions, FEM simulations and experimental data demonstrates the ability of the proposed method to accurately simulate the speaker performances, thus representing a fast tool for the design of this class of MEMS speakers.