In this study the three-dimensional free vibration analysis and modal stress analysis of an adhesively bonded composite single lap joint having unidirectional laminated narrow plates and subjected to clamped-free condition are carried out. The first ten natural frequencies and mode shapes of the adhesive joint are considered. The effects of fiber angle, fiber volume fraction, overlap length, and plate thickness on the natural frequencies and the mode shapes of the adhesive joint are investigated using the back-propagation artificial neural network (ANN) method. A series of free vibration and stress analyses is carried out using the finite element method for random values of the fiber angle, the fiber volume fraction, the overlap length, and the plate thickness so that the proposed ANN model can be trained successfully to predict the first ten natural frequencies as well as the corresponding modal strain energies. The ANN models indicate that the fiber angle is a more dominant parameter than the fiber volume fraction on the natural frequencies and the corresponding mode shapes of the adhesive joint, and the plate thickness and the overlap length are important geometrical design parameters whereas the adhesive thickness has a minor effect. In addition, genetic algorithm is combined with the present ANN model to achieve the optimal joint design which satisfies maximum natural frequency and minimum modal strain energy conditions for each natural frequency and mode shape of the adhesively bonded composite single lap joint.