A bonded plate or a coated part can be debonded by external impact or thermal expansion. To analyse adhesive strength, the blister test is generally adopted. In this paper, a blister test is modelled theoretically and then the stability and bifurcation of the blister are studied under several different cases. The blister is simplified to consist of a pure bending plate attached elastically to the rigid substrate. Expression of the energy release rate is obtained as a form of an explicit function for a circular-type blister or tunnel-type blister grown by controlling the internal pressure or internal volume. Stability and bifurcation are also studied in the frame of the quasi-static evolution. The study shows that the circular- type blister propagates with the first mode of bifurcation and that the tunnel-type blister propagates with a regular wave. It is proved that the waves have the same form on two side lines of the tunnel and that the wave length can be obtained. When the internal pressure is controlled, the blister is unstable, but when the internal volume is controlled, it is stable.