Functionally modulus graded bondline (FMGB) adhesives can be employed in bonded joints to reduce stress concentration and, hence, achieve higher joint strength. This study presents an analytical framework for the stress analysis of a shaft-tube bonded joint based on a variational technique which minimises the complimentary energy of the bonded system. This cylindrical assembly consists of similar or dissimilar adherends and a FMGB adhesive. The effect of functional grading of adhesive elastic modulus on the peak stresses and their distributions in the adhesive layer are studied. The joint with various modulus grading profiles is assessed and the results are compared with a conventional mono-modulus bondline (MMB) adhesive joint. Stress analysis indicates that the peel and shear peak stresses in the FMGB are much smaller and their distributions along bondlength are more uniform than those of MMB adhesive joints under the same axial tensile load. Numerical examples are provided to illustrate the effects of geometrical and material properties on the distributions and intensities of stresses in the bondline. Furthermore, optimal peel and shear strengths of the joint can be achieved by spatially controlling the modulus of the adhesive.