Robots may suffer from excessive internal force in contact tasks especially when they are position-controlled or executing complicated assemblies. Excessive internal force will lead to failure of the tasks, so it is important to predict and avoid such situations. This paper presents mechanical analysis of internal force applied to objects in robotic manipulation. A linear-programming-based algorithm that can judge the possibility of excessive internal force under Coulomb friction is proposed. Numerical examples including an internal force problem in graspless manipulation and a wedging problem in peg-in-hole are also showed. Our algorithm will help the planning of robotic contact tasks.