This study investigates the three-dimensional free vibration behaviour of an adhesively bonded functionally graded single lap joint. The functionally graded plates of the adhesive joint are composed of ceramic (Al2O3) and metal (Ni) phases varying through the plate thickness. The effects of geometrical parameters, such as plate width, plate thickness and overlap length, especially the effect of the similar and dissimilar material composition variations through-the-thicknesses of both upper and lower plates on the natural frequencies and corresponding mode shapes of the adhesive joint were also investigated using both the finite element method and the back-propagation artificial neural network (ANN) method. A series of the free vibration analyses were carried out for various random values of the geometrical parameters and the through-the-thickness material composition so that a suitable ANN model could be trained successfully. The proposed ANN models indicated that increasing plate thickness and compositional gradient exponent resulted in increases in the first 10 frequencies whereas the overlap length has negligible effect. In contrast, the natural frequencies decrease suddenly with increasing the plate width. For the plate width > 50 mm, the natural frequencies become very low and the effect of the other design parameters on the natural frequencies becomes minor. In case the upper and lower plates have similar or dissimilar material composition variations the mode shapes were affected considerably, but the natural frequencies. (C) 2009 Elsevier Ltd. All rights reserved.