Vibration of thin piezoelectric and conducting plates in different electric and magnetic fields, respectively, is investigated. Specifically, the dominant trends in the frequency-thickness dependence have been examined in detail for both types of plates made of multifunctional materials and with different plate-end conditions. For anisotropic piezoelectric materials, the effects of key material parameters (such as piezoelectric coefficients) on the in-field geometry changes and the resulting vibration frequency shifts are evaluated. A new model for the geometry-based corrections to the in-field vibration frequencies is presented for a piezoelectric plate in an electric field. The frequency results are presented for various piezoelectric polymers to illustrate the influence of material properties on the in-field vibration frequency. A second analytical model is developed for the in-field vibration of isotropic conductive plates in magnetic fields. This model captures phenomenologically the vibration frequency shifts by means of an effective "in-field thickening" of the conductive plates. Frequency predictions obtained by using this model compare favorably with the available theoretical results for the vibration of perfectly conducting plates over a wide range of thickness-tolength ratios.