This study reports the most effective design parameters for the three-dimensional free vibration and modal stress state of an adhesively bonded cantilevered composite tubular single lap joint. The effects of fibre angle, fibre volume fraction, overlap length, tube thicknesses and inner tube radius on the first ten natural frequencies and mode shapes of the adhesive tubular joint were investigated, using the back-propagation Artificial Neural Network (ANN) method. In order to train and test the proposed artificial neural network models used to predict the first ten natural frequencies, as well as the corresponding modal strain energies, a series of free vibration and stress analyses was carried out. The finite element method was used for random values of the design parameters, such as the fibre angle, the fibre volume fraction, the overlap length, the tube thicknesses and the inner tube radius. The ANN models indicated that increasing each of all the design variables resulted in increases in the first ten natural frequencies as well as in the modal strain energies, whereas increasing the inner tube thickness reduced the natural frequencies but increased the modal strain energies. The fibre angles above 20 degrees and the inner tube radius were more effective design parameters than the overlap length and the outer tube thickness. The Genetic Algorithm indicated completely different values of the design parameters of an optimal joint based on three objective functions, in which i) the natural frequency only was maximised, ii) the modal strain energy was minimised and iii) the previous objective functions were balanced. Thus all design parameters were maximised as possible except the inner tube thickness, and the fibre volume fraction became optimal at 70%.