The determination of material symmetries and principle plane orientations of anisotropic plates, whose planes of symmetries are not known apriori, were calculated using a Genetic Algorithm (GA) based blind inversion method. The ultrasonic phase velocity profiles were used as input data to the inversion. The assumption of a general anisotropy was imposed during the start of each blind inversion. The multi-parameter solution space of the Genetic Algorithm was exploited to identify the "statistically significant" solution sets of elastic moduli in the geometric coordinate system of the plate, by thresholding the coefficients-of-variation (Cv). Using these "statistically significant" 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. This procedure was verified using simulated ultrasonic velocity data sets on material with orthotropic symmetry. Experimental validation was also performed on unidirectional Graphite Epoxy 7s fiber reinforced composite plate. © 2007 American Institute of Physics.