This article presents a stability analysis of object grasping with a compliant multi-fingered robot hand. This stability analysis is based on an energetic approach, in which we aim to compute the maximum amount of energy that can be stored by a compliant hand-object system about a stable equilibrium before being destabilized. More specifically, the case of external disturbance wrenches is investigated. This analysis admits several applications, two of which are illustrated in this article on a case study. First the quality of a given grasp can be quantified in terms of maximum allowed disturbance force and the associated displacement around the initial equilibrium, with applications in trajectory design for the robot arm that holds the hand-object system. Conversely, given a task specified in terms of known disturbance wrenches set, the proposed approach helps determining the optimal grasp for an enhanced stability, e.g. the contact points locations, joint compliance or internal forces levels.