The overlapping contact configuration model of carbon nanotubes in polymer matrix is proposed. The effects of conductivity and mass fraction of carbon nanotubes as well as polymer, geometric parameters of carbon nanotubes, and the electrical tunneling effect due to a small region of the polymer matrix material filling the gap at the nanotubes junction on the conductive properties of carbon nanotubes polymer composites are discussed in detail. The conductivity formula of the composites is deduced. The conductivity log-arithms of multiwalled carbon nanotubes phenoxy compositie and multiwalled ca...