While suction technology was invented long ago, the application of suction to object manipulation thus far has been confined to many small, well-defined problem sets. Its potential for grasping a large range of unknown objects remains relatively unexplored. This paper introduces the design of a suction cup that is “self-sealing.” The suction cups comprising the grasper exert no suction force when the cup(s) are not in contact with an object, but instead exert suction force only when they are in physical contact with an object. Since grasping is achieved purely by passive means, the cost and weight associated with individual sensors, valves, and/or actuators are essentially eliminated. This paper presents the design, analysis, fabrication, and experimental results of an array of such self-sealing suction cups. Finite element analysis of the cup is shown for both compressive and tensile loading, and the quality of the internal seal is quantified. Finally, performance is shown to be comparable to that of a commercially available cup, and grasping capability is demonstrated on a wide range of objects.