Described herein are flexible truss systems and methods of transferring flexible composite parts using these systems. A flexible truss system comprises a flexible truss mechanism and composite pick-and-place mechanisms supported on the flexible truss mechanism and designed to attach to various composite parts. The flexible truss mechanism comprises flexible elongated members and slidable ribs coupled to each flexible elongated member. Specifically, each rib is slidably coupled to at least one flexible elongated member. In some examples, each rib is also fixedly coupled to another flexible elongated member. The slidable coupling allows the flexible truss mechanism to bend and follow the shape of a supported part, such that the composite pick-and-place mechanisms are able to contact and support different areas of the composite part. As such, the same flexible truss mechanism is able to support flexible composite parts having different shapes.