Numerical inversion of the Hankel–Laplace transform has been performed for the case of ultrasonic displacements in an infinite, homogeneous, isotropic plate which is excited thermoelastically by a laser pulse. Values for the elastic moduli and the plate thickness may be extracted when the calculated displacements are compared directly to those obtained experimentally. Previous authors have demonstrated methods for determining the elastic modulus in thick plates; this letter shows that using a different method for the development of the theory allows similar modulus determinations to be made for thin as well as thick plates.