The determination of material symmetries and principle plane orientations of anisotropic plates, whose planes of symmetries are not known, are calculated using a Genetic Algorithm (GA) based blind inversion method. Ultrasonic phase velocity profiles were used as input data to the inversion. During each blind inversion, the material was initially assumed to be dependent on 21 elastic moduli (general anisotropy). A Genetic Algorithm based method was exploited to identify the "statistically significant" elastic moduli using the coefficient of variation (CV) to derive a reduced set of elastic moduli. The unknown material symmetry and the principle planes (angles between the geometrical coordinates and the material symmetry coordinates) were evaluated using the method proposed by Cowin and Mehrabadi [Cowin SC, Mehrabadi MM. On the identification of material symmetry for anisotropic elastic materials. Quart J Mech Appl Math 1987;40(4):451-76], Cowin [Cowin SC. Properties of the anisotropic elasticity tensor. Quart J Mech Appl Math 1989;42(2):249-66] and Sun [Sun M. Optical recovery of elastic properties for a general anisotropic material through ultrasonic measurements. M.S. thesis, The Graduate School, University of Maine, August 2002]. This procedure was verified using simulated ultrasonic velocity data sets on materials with transversely isotropic, orthotropic, monoclinic and triclinic symmetries. Experimental validation was also performed on a unidirectional graphite-epoxy 7s material, a quasi-isotropic graphite-epoxy [0/45/90/-45]7s fiber reinforced composite plate, and plate cut at 45° to the fibers from a unidirectional graphite-epoxy composite plate. © 2007 Elsevier Ltd. All rights reserved.