A key challenge in robotics is to create efficient methods for grasping objects with diverse shapes, sizes, poses, and properties. Grasping with hand-like end effectors often requires careful selection of hand orientation and finger placement. Here, we present a fingerless soft gripper capable of efficiently generating multiple grasping modes. It is based on a soft, cylindrical accordion structure containing coupled, parallel fluidic channels, which are controlled via pressure supplied from a single fluidic port. Inflation opens the gripper orifice for enveloping an object, while deflation allows it to produce grasping forces. The interior is patterned with a gecko-like skin that increases friction, enabling the gripper to lift objects weighing up to 20 N. Our design ensures that fragile objects, such as eggs, can be safely handled, by virtue of a wall buckling mechanism. In reverse, the gripper can be deflated to reach into an opening or orifice then inflated to grasp objects with handles or cavities. The gripper may also integrate a lip that enables it to form a seal and, upon inflating, to generate suction for lifting objects with flat surfaces. In this article, we describe the design and fabrication of this device and present an analytical model of its behavior when operated from a single fluidic port. In experiments, we demonstrate its ability to grasp diverse objects, and show that its performance is well described by our model. Our findings show how a fingerless soft gripper can efficiently perform a variety of grasping operations. Such devices could improve the ability of robotic systems to meet applications in areas of great economic and societal importance.