An important challenge in robotics is to achieve robust performance in object grasping and manipulation, dealing with noise and uncertainty. This paper presents an approach for addressing the performance of dexterous grasping under shape uncertainty. In our approach, the uncertainty in object shape is parameterized and incorporated as a constraint into grasp planning. The proposed approach is used to plan feasible hand con gurations for realizing planned contacts using different robotic hands. A compliant nger closing scheme is devised by exploiting both the object shape uncertainty and tactile sensing at ngertips. Experimental evaluation demonstrates that our method improves the performance of dexterous grasping under shape uncertainty.