Carbon nanotubes (CNTs) have been regarded as ideal reinforcements for high-performance composites. A key factor for the reinforcement efficiency is the interface bonding between the CNTs and the matrix. This paper presents a new constitutive model to predict the mechanical performance of composites made with CNTs. The model takes into account explicitly the performance of the interface between the matrix and the CNTs. The formulation developed is based in the mixing theory. It divides the composite in matrix and in a new material result of coupling the CNTs with the interface. The relation defined between interface and CNTs assumes that the load is transferred to the nanotubes along their ends and that in the central part the CNTs can develop their full strength. The composite non-linear behavior results from the non-linearities of its constituents. In case of interface damage, it also becomes non-linear the law defined to couple the interface with the CNTs. After describing the formulation, it is validated studying the elastic response of several composites made with different types of CNTs reinforcements. The non-linear behavior provided by the formulation is also studied. In both cases the numerical results are compared with experimental data showing good agreement.