The rate of propagation of embedded delamination in the strap adherend of lap shear joint (LSJ) made of carbon/epoxy composites has been evaluated employing three-dimensional non-linear finite elements. The delamination has been presumed to pre-exist in the thin resin layer between the first and second plies of the strap adherend. The inter-laminar peel and shear stress distributions have been studied in details and are seen to be predominantly three-dimensional in nature. The components of strain energy release rate (SERR) corresponding to the opening, sliding and cross sliding modes of delamination are significantly different at the two fronts of the embedded delamination. The sequential release of multi-point constraint (MPC) finite elements in the vicinity of the delamination fronts enables to simulate the growth of the delamination at either ends. This simulation procedure can be utilized effectively for evaluation of the status of the structural integrity of the bonded joints.