Systems and methods are provided for shape controlled gripping of a workpiece. A layer jamming structure includes a membrane defining an internal cavity containing a number of overlapping material layers. A pressure system includes a pump coupled with the internal cavity. A shape conforming tool includes at least one part configured to move to apply a force to the layer jamming structure. The shape conforming tool, by operation of the part, conforms the layer jamming structure to the workpiece. The pressure system, with operation of the pump, changes a pressure in the internal cavity to impart rigidity to the layer jamming structure.