Carbon nanotubes (CNTs) has become a paradigm for studying electronic transport on low dimensions. They have a high potential for applications in the emerging field of molecular electronics. The main body of research on electronic transport in CNTs in the last decade has mainly focused on elastic transport. The influence of vibrational excitations on charge propagation in CNTs has not been however addressed in detail. We present a density-functional-based study on the influence of structural lattice fluctuations on the elastic electronic transport in carbon nanotubes in the linear response regime. Structural distortions are considered as a random field; the linear conductances can be calculated after appropriate averaging over this field. Results obtained from a frozenphonon- like approximation are compared with classical molecular dynamics simulations. We demonstrate that the average effect of structural fluctuations can be captured by the Anderson model of disorder. Further, the influence of single vibrational modes on the electronic transport can be extracted with our approach as well as the role of zero-point quantum fluctuations.