A self-supporting system for positioning and restraining the U-bend tubes in the U-bend region of a nuclear steam generator includes arrays incorporating unique support bars having nubs projecting in the out-of-plane direction of the tube planes. The system also includes assemblies for spacing the arrays, tie bars to prevent the arrays from splaying and saddle bar assemblies to support the outermost tube layers. The system provides positive restraint to nub engaged tubes in both the in-plane direction of the tube planes and the out-of-plane direction.