Robot grasping of deformable hollow objects such as plastic bottles and cups is challenging, as the grasp should resist disturbances while minimally deforming the object so as not to damage it or dislodge liquids. We propose minimal work as a novel grasp quality metric that combines wrench resistance and object deformation. We introduce an efficient algorithm to compute the work required to resist an external wrench for a manipulation task by solving a linear program. The algorithm first computes the minimum required grasp force and an estimation of the gripper jaw displacements based on the object’s empirical stiffness at different locations. The work done by the jaws is the product of the grasp force and the displacements. Grasps requiring minimal work are considered to be of high quality. We collect 460 physical grasps with a UR5 robot and a Robotiq gripper. We consider a grasp to be successful if it completes the task without damaging the object or dislodging the content. Physical experiments suggest that the minimal work quality metric reaches 74.2% balanced accuracy, a metric that is the raw accuracy normalized by the number of successful and failed real-world grasps, and is up to 24.2% higher than classical wrench-based quality metrics.