Abstract: Provided are end effectors and methods of using such end effectors for handling various composite structures. An end effector includes a support structure bendable relative the principal axis of the end effector. The support structure is disposed within a cavity partially formed by an engaging portion of the end effector. The engaging portion is formed from a flexible material and includes multiple openings in fluid communication with the cavity. When the engaging portion contacts a composite structure and when the pressure inside the cavity is reduced below the ambient level, the composite structure is forced against the engaging portion due to this pressure differential. The flexibility of the support structure and of the engaging portion allows the end effector to conform to the shape of the composite structure. At the same time, the support structure maintains the shape of the cavity in the directions normal to the principal axis.