Development of soft robotic devices with grasping capabilities is an active research area. The inherent property of soft materials, to distribute contact forces, results in a more effective robot/environment interaction with simpler control. In this paper, a three-finger under-actuated adaptable soft gripper is proposed, highlighting the design and manufacturing process. A novel design and actuation principle have been implemented to obtain the desired grasping abilities, from mechanical properties of materials and structures. Soft materials have been used to make each finger, for a high adaptability of the gripper to different shapes. We implemented an under-actuated mechanism through a wire loop actuation system, that helps achieving passive adaptation during grasping. Passive adaptability allows to drive the device with a reduced number of control parameters. The soft gripper has been lodged into an experimental setup endowed with one actuation unit for the synchronous flexion of its fingers. Grasping and holding capabilities have been tested by evaluating the grasp stability with target objects varying in shape, size and material. Adaptability makes this soft device a good application of morphological computation principles in bio-inspired robots design, where proper design of mechanical features simplifies control.