Advances in material science in recent years have had such a tremendous impact on the field of soft robotics that has fostered the development of many bio-inspired devices. One such device, which has been subject to extensive study in recent times, is soft pneumatic-network (pneu-net) actuators (SPAs). In this study, we present a new SPA structure whose chamber configuration mimics the fish bone (herringbone) structure to facilitate simultaneous bending deformations in both longitudinal and transverse directions. Such as cannot be obtained from the regular pneu-net structure – which bends only lengthwise, the coupled bending curvatures allow for gripping with maximized contact area, a property which facilitates firmness, security, and stability in gripping. Using the corresponding chamber inclination angle of the configuration as key parameter, the combined transverse and longitudinal deformation feature is studied through finite element simulation as well as experiments. Also, the functional behavior of the actuator/gripper prototypes is experimentally investigated using a series of approaches including blocked (or tip) force test, grip strength test, and stability (or sustained grasping force) test. Furthermore, the viability of the said conformal gripping characteristic is demonstrated by subjecting the structure to a couple of gripping tests. This utility-enhancing design approach could really guide into the development of more sophisticated application-custom soft robotic capabilities.