Many industries such as oil, gas, aerospace, and automotive, use axisymmetric adhesively bonded single lap joints. Different materials are frequently mated using axisymmetric lap joints. When composite adherents delaminate, the stress circulation inside the adhesive layer significantly influenced. As a result, the importance of considering adhesive layer stresses in the presence of considerable delamination is investigated in this paper. To understand stress analysis and examine adhesive bond strength at static loading conditions, the model created using finite element analysis with cohesive zone modelling. A complete parametric study carried using simple finite element code in ABAQUS, the axisymmetric single lap joins adhesively bonded joints prepared with different material adherents. Analysis carried on the influence of numerous factors such as the distribution stress inside the adhesive joints. In this connection, mating of carbon reinforced polymer composite to titanium alloy adherends discussed thoroughly. The results show that depending on the position of the delamination, the presence of a throughout-the-thickness delamination affects the structural response of both single lap and axisymmetric adhesively bonded joints by varying overlap length. The presence of a delamination reduced adhesive peel and shear stresses significantly in both joint configurations.