This study investigates elastic stresses in the adhesive layer and tubes of an adhesively bonded tubular joint with functionally graded (Ni-Al2O3) tubes subjected to an internal pressure. A 3D eight-noded isoparametric multilayered finite element with three degrees-of-freedom was used to model the tubes composed of a functionally gradient layer between a ceramic layer and a metal layer. The hoop stress in the tubes and the radial stress in the adhesive layer were dominant among the stress components. Both free edges of the adhesive layer were subjected to considerable stress concentrations whereas a large area in the middle of the overlap region experienced relatively low uniform stress levels. In addition, the stress concentrations were observed through the thickness of the outer and inner tubes corresponding to the adhesive free edges. Thus, the outer-tube regions close to the left free edge of the adhesive layer and the inner-tube regions close to the right free edge of the adhesive were subjected to relatively high stress levels. The highest stresses occur in the ceramic zones of both outer and inner tubes, and decrease through the tube thickness towards the metal zones. The free edge of the outer tube-adhesive interface and the right free edge of the inner tube-adhesive interface were the most critical regions. Increasing the layer number through the thickness of the tubes (higher than 40 layers) had a negligible effect on the magnitude of von Mises stresses in the ceramic and metal rich zones of both functionally graded outer and inner tubes and on the peak adhesive stresses. The through-thickness profiles of von Mises stresses are not affected by the layer number. However, increasing the ceramic phase in the material composition through the tube thickness based on the power law affects evidently both through-thickness profile and magnitude of von Mises stresses in the ceramic and metal zones of both tubes and inside the adhesive layer. Thus, as the compositional gradient exponent is increased between 0.1 and 10, the peak stresses in the ceramic zone decrease by 42%, whereas the peak stresses in the metal zone exhibit negligible increases. The through-thickness profiles of von Mises and hoop stresses become similar as the ceramic phase is increased. However, the stress profiles across the adhesive layer remain the same whereas von Mises and hoop stress levels at the adhesive-outer tube interface and at the adhesive-inner tube interface decrease uniformly (47%). Accordingly, only the compositional gradient exponent has a considerable effect on the stress state of the functionally graded tubular structures subjected to external loads contrary to the thermal loads.