Analytical solutions for circular membranes with different boundary conditions are obtained based on the assumptions of large displacements, small rotations, and small strains. The solutions take into account prestresses of arbitrary magnitude. The maximum stresses and strain energy release rates for the standard and island blister tests are obtained. The fracture efficiency parameter, defined as the ratio between the strain energy release rate and the square of the maximum stress, is then introduced to study the geometric effect on the relationship between the failure along the interface and in the coating. The fracture efficiency parameter is also used to find the optimal specimen dimensions for a given blister test geometry. It is found that the prestresses have a significant effect on the parameter. Although the island blister test is capable of producing very high strain energy release rates at relatively low pressures by decreasing the size of the island, the fracture efficiency parameter does not increase because of the significant increase of stress at the edge of the island. No significant difference in the fracture efficiency parameter is found between the standard and island blister geometries. The result suggests that yielding is likely to take place in all blister test methods at about the same applied strain energy release rate for a given film thickness and properties.