We present a study of the behavior of highly ordered, segregated single-wall carbon nanotube (CNT) networks under applied strain. Polymer latex templates induce self-assembly of CNTs into hexagonal (2D) and honeycomb (3D) networks within the matrix. Using mechanical and spectroscopic analysis, we have studied the strain transfer mechanisms between the CNT network and the polymer matrix. Axial deformation of the nanotube network under applied strain is indicated by downshifts in the 2D mode in the Raman spectra, as well as variation in the radial breathing modes.The slippage within nanotube bundles at high strain is indicated by a reduction in the 2D mode rate of change. The fractional resistance change of the composites with strain obeys power law dependence. We present a model for the behavior of CNT bundles under strain informed by these measurements, and potential applications for such composite materials in elastic electronic devices that can tolerate high strain.