In this study, the three-dimensional free vibration analysis of an adhesively bonded functionally graded tubular single lap joint was carried out using the finite element method. The functionally graded tubes of the adhesive joint are composed of ceramic (Al2O3) and metal (Ni) phases varying through the tube thickness. The adhesive material properties, such as modulus of elasticity, Poisson's ratio, and density were found to have negligible effect on the first ten natural frequencies and mode shapes of the adhesive joint. The optimal design parameters of the adhesive joint, such as overlap length, inner radius of the inner tube, outer and inner tube thicknesses, and the through-the-thickness material composition variation were searched using both the artificial neural networks (ANNs) and the genetic algorithms (GAs). For this purpose, the natural frequencies and modal strain energy values were calculated for an adhesive joint with random geometrical properties and material compositions through the tube thicknesses, and were used for training the proposed artificial neural network models. The outer tube thickness, the inner tube-inner radius, and the compositional gradient exponent had considerable effect on the natural frequencies, mode shapes, and modal strain energies of the functionally graded tubular single lap joint, whereas the overlap length and the inner tube thickness had a minor effect. The GAs integrated with ANNs was employed to determine optimal design parameters satisfying both maximum natural frequency and minimum modal strain energy conditions for each natural mode of the tubular adhesive joint.