This study investigates the three-dimensional free vibration behaviour of an adhesively-bonded corner joint with single support. The modulus of elasticity, Poisson's ratio and density of adhesive were found to have negligible effects on the first 10 natural frequencies and mode shapes of the corner joint. The effects of the geometrical parameters, such as support length, plate thickness, adhesive thickness and joint length, on the natural frequencies, mode shapes and modal strain energies of the adhesive joint were also investigated using both the finite element method and the back-propagation artificial neural network (ANN) method. The free vibration and stress analyses were carried out for the corner joints with various random geometrical parameters so that a suitable ANN model could be trained successfully. The support length, plate thickness and joint length all played important roles in the natural frequencies, mode shapes and modal strain energies of the corner joint, whereas the adhesive thickness for the range of adhesive thickness studied had only a minor effect. The Genetic Algorithm was also combined with the present ANN models in order to determine the optimum geometrical dimensions which satisfied the maximum natural frequency and minimum modal strain energy conditions for each natural frequency and mode shape of the adhesively-bonded corner joint.