© 2015 American Scientific Publishers All rights reserved Printed in the United States of America. The potential use of carbon nanotubes based composites as structural materials in hazardous radiation environments calls for investigating their radiation damage resistance. In this study molecular dynamics simulations were utilized to elucidate the keV protons-induced processes in composites comprising carbon nanotubes and polyethylene chains. In particular, the investigation is focused on revealing the effect of the carbon nanotubes chiralities on the composite radiation damage tolerance and the composite's surviving stiffness. Radiation was emulated by adding an explicit energy term to that calculated via a force field which drove the systems away from thermodynamics equilibrium. It was observed that the damage accumulates rapidly during the early stages of the simulation and it consisted mostly of polyethylene chain scissoring and generation of small hydrocarbon radicals. Evident by the number of defragmentation and the endured elastic stiffness, composites incorporating carbon nanotubes with zigzag or armchair structure were found to be more resistant to radiation damage than those utilizing nanotubes with intermediate chiralities.