Yarns and fabrics are subjected to a low level of stresses or strains of repetitive nature in processing and actual use which leads to breakage, permanent deformation, bagging and loss of useful life of the product. The ability of the spun yarns and fabrics to withstand such stresses depends upon their structural integrity. A structurally rigid yarn (i.e. yarns in which fibres are tightly bound) would behave more like an elastic solid and consume more energy during deformation as the constituent fibres have to be deformed. Once the strain is released, the recovered energy will also be more. On the other hand if the structural integrity of the same yarn is poor, fibres would easily slip during deformation and would consume much less energy. The recoverable energy also will be much less. The present investigation reports on the structural integrity of friction spun yarns in terms of energy loss or decay by employing cyclic extension test. It has been observed that friction spun yarns in which the core is immediately wrapped by long and strong polyester fibre layer make the structure strongest as polyester is expected to form tight wrappings. The decay in deformation energies during extension cycling depends upon sheath structure i.e. its composition and location of constituent fibres in sheath layers. With increase in core fibre %, the decay has been found to increase. However, the decay values discriminate more between core% differences than between sheath fibre layer arrangements.