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Modern MEMS transducers frequently employ electrostatic transduction with perforated plates. Despite the prevalence of these devices, 3D numerical simulations of their structural vibrations remain computationally expensive, and a clear analytical understanding of the underlying physics is often lacking. This paper addresses these challenges by providing analytical approximations for the eigenfrequencies of clamped non-perforated and perforated square plates.Using symbolic regression, we provide analytical approximations while avoiding the instabilities associated with high-degree polynomials. For perforated plates, the eigenfrequency is modeled as a normalized discrepancy to the solid case using a rational function characterized by only two geometry-dependent parameters. This sparse, interpretable form facilitates the subsequent derivation of the effective Young’s modulus and effective plate density. To the best of our knowledge, this is the first work to employ symbolic regression for the analytical approximation of perforated plate eigenfrequencies.