The development of soft pneumatic actuators based on composites consisting of elastomers with embedded sheet or fiber structures (e.g., paper or fabric) that are flexible but not extensible is described. On pneumatic inflation, these actuators move anisotropically, based on the motions accessible by their composite structures. They are inexpensive, simple to fabricate, light in weight, and easy to actuate. This class of structure is versatile: the same principles of design lead to actuators that respond to pressurization with a wide range of motions (bending, extension, contraction, twisting, and others). Paper, when used to introduce anisotropy into elastomers, can be readily folded into 3D structures following the principles of origami; these folded structures increase the stiffness and anisotropy of the elastomeric actuators, while being light in weight. These soft actuators can manipulate objects with moderate performance; for example, they can lift loads up to 120 times their weight. They can also be combined with other components, for example, electrical components, to increase their functionality.