The hysteresis behaviour of multigraft (MG) copolymers, with a polyisoprene backbone and polystyrene (PS) side chains, was investigated by applying a modified softening model proposed by Elias-Zuniga, which uses an approach of Ogden and Roxburgh. The model was combined with the non-affine tube model of rubber elasticity of Kaliske and Heinrich. Four parameters are obtained: chemical and physical cross-link moduli (G(c), G(e)) the number of statistical segments between two successive entanglements (n(e)/T-e) and a softening parameter (b). The model was proven to be valid by a comparison with other methods evaluating hysteresis behaviour The characterization of the multigraft copolymers revealed a branch point and molecular architecture dependence of the softening parameter. b was low for tetrafunctional MG copolymers with cylindrical microdomains, and it was further reduced for a spherical morphology and for more complex Molecular architectures. The magnitude of b also depends on the PS arm molecular weight for hexa- and tetrafunctional multigraft copolymers. (C) 2009 Elsevier Ltd. All rights reserved.