When a robot is constrained by more than one inequality constraints, the analysis of the contact force becomes quite involved. Moreover, the degree‐of‐freedom of the robot motion is reduced in a constrained motion. Frequently, it is desirable to analyze the motion behavior of the robot before, at, and after the contact instant. In our previous report, a robot with one inequality constraint was carefully examined. In this paper, we extend our results to the case of a robot with two inequality constraints. The mathematical model, the impact force, the elasticity and friction of the constraint surface will be discussed. In addition, a solution algorithm will be developed for the model.