The mechanical properties of braided carbon nanotube yarns (CNTYs) on elastomeric core hybrids have been modeled and studied under tension. The model predicts the stress-strain behavior of the composite as a function of the initial braiding angle (BA) and the number of pitches. Two innovative aspects were included in the model. The first relates to the friction between the braid and the core, and the second includes the change in the core diameter due to the braid compression stresses on the core. Results indicate good agreement between the theoretical model and the experimental results. Since the diameter rate decrease, of the CNTYs braid, is higher than that of the elastomeric core diameter, a 'squeezing out of the core through the braid inter yarn space occurs. Thus, a critical strain may be defined where the braid comes in contact with the core. Moreover, the friction play as significant contributes to the model conformity to the experimental results. As the CNTYs are conductive, a stretchable conductive composite is obtained having a resistivity of 0.004 Ohm*cm, which remains constant throughout the tensile loading to failure and under cyclic loading.