This paper proposes a unified model for investigating the vibration and acoustic radiation behaviors of magneto-electro-thermo-elastic functionally graded porous plates (METE-FGPPs). The model is established by first-order shear deformation theory (FSDT) combing with the Voigt model and modified power-law distribution. For the sake of simplicity, the formulations with regard to the vibration and acoustic radiation of METE-FGPPs are deduced by using the Rayleigh-Ritz method, and many fields including mechanical, magnetic, electrical and thermal fields are taken into account. Meantime, it is worth noting that the penalty functions are introduced into this model for satisfying the mechanical and magneto-electric boundaries easily. For improving the convergence, accuracy, stability of numerical calculation, the displacement functions of METE-FGPPs are expressed by adopting Chebyshev polynomials. Based on the established unified model, the investigations of the vibration and acoustic radiation characteristics of METE-FGPPs are realized in the following discussion. Firstly, the convergence of the presented method is verified by investigating the convergence of truncated number, number of elemental radiator and penalty factor. Secondly, the accuracy, stability and versatility of the presented approach is confirmed by comparing with the results of existing literatures. Finally, the influence of some key parameters on the vibration and acoustic radiation of METE-FGPPS are discussed carefully.