Abstract The effect on stiffness and debonding of an interphase zone of altered polymer properties surrounding each carbon nanotube (CNT) in a CNT reinforced polymer composite is investigated. The interphase zone has position dependent material properties that merge with those of the polymer at a sufficiently large distance from the inclusion. There is evidence that such an interphase zone must be included in models in order to represent the overall composite properties. The analyses are based on an axisymmetric unit cell model of the composite. An elastic–viscoplastic conventional continuum constitutive relation (a size-independent relation between stress, strain and strain rate) is taken to characterize the bulk polymer material and the interphase, with the material properties being position dependent in the interphase. The interface between the polymer and the CNT is modeled by a phenomenological cohesive relation that allows for complete separation and the creation of new free surface. The effect of varying interface strength on the composite stress–strain response and on debonding is analyzed both with and without an interphase. The presence of an interphase increases the composite stiffness but promotes debonding which ultimately reduces composite stress carrying capacity. The compliance of the interface also affects the stress–strain response prior to debonding and leads to stress redistributions within both the fiber and the matrix (and/or interphase) which can affect the fracture mode that occurs.