In this paper we present a nondestructive method for determining the elastic constants of thin isotropic plates using poly(vinylidene fluoride–trifluoroethylene) [P(VDF–TrFE)] copolymer ultrasound focusing transducers and Lamb wave measurements. Lensless P(VDF–TrFE) line-focus transducers are fabricated, and Lamb wave defocusing measurements are performed to measure the multimode Lamb wave dispersion curves of stainless steel and glass thin-plate samples of thicknesses ranging from 100 to 250 µm. Dispersion-curve-sensitivity analysis is carried out to determine the best method of inverse determination of the elastic properties. A search method based on the downhill simplex algorithm is applied to inversely determine the elastic constants of isotropic plate samples. The obtained results are in good agreement with the data reported by the manufacturers. Measurement accuracy and potential applications of the P(VDF–TrFE) ultrasound focusing transducers and measurements for other types of nondestructive evaluation are addressed.