The classical problem for a partially debonded circular inhomogeneity is revisited. The interaction of the interfacial crack and a point singularity such as a point force and/or a dislocation is dealt with. Also the circular arc-shaped interfacial crack under remote stress is solved. This problem has been solved by many researchers for the cases of various loading types. However, lack of generality in the solution technique together with too complicated form of the solution makes it hard to grasp the structure of the solution. Based on the recently published technique for a perfectly bonded circular inhomogeneity, this problem is revisited. The resulting form of the solution is very simple, therefore, its structure is easily understood. Due to the merit of the present method, the image force on the edge dislocation near the tip of the interfacial crack is easily obtained.