In this paper, we present the analysis of grasp stability for multi-fingered robot hands that is based on translational and rotational acceleration convex polytopes. The aim of the grasp stability analysis is to find the resistance forces and moments of robot hands that can withstand the external disturbance forces and moments applied on objects. We calculate the resistance forces and moments respectively which are considered the properties of objects and robots. Therefore, the resistance forces and moments depend on the joint driving torque limits, the posture and the mass of robot fingers, the configuration and the mass of objects, the grasp position, the friction coefficients between the object surface and the end-effectors of robot fingers. We produce the critical resistance force and moment which are absolutely stable about external disturbances in all directions, the global resistance force and moment which are whole grasp capability of robot hands, and the weighted resistance forces and moments which can be properly used by controlling two indices according to the importance of robot hands. The effectiveness of this method is verified with simulation examples.