Some closed-form equations for the coupling problem of buckling and growth of circular delamination are derived by recourse to the moving boundary variational principle The axisymmetric buckling of a circular delamination subjected to an equal bi-axial compression is analysed by using high-order perturbation expansion The axisymmetric buckled delamination has the following properties: under a certain residual pressure, there exist two characteristic radii, namely the critical radius Rc and growing radius Rg; for a certain interface toughness, the blister has three configuration of stationary, stable growth and unstable growth with increasing the loads Under a higher edge thrust, the nonaxisymmetric secondary buckling will occur on the base of axisymmetric buckling and then the toughness and the driving force of the interface crack will be different along the delamination front. So the growth of circular delamination will not be self-similar. Without any assumption regarding the delamination front, the cogfigurations of the blister with several nonaxisymmetric buckling modes n=2, 3, 6, 8, are simulated. The nonaxisymmetric growth process for the nonaxisymmetric buckling mode n=2 is simulated also under a sequence of loads.