The complex structure of the macroscopic assemblies of carbon nanotubes and variable intrinsic piezoresistivity of nanotubes themselves lead to highly interesting piezoresistive performance of this new type of conductive material. Here, we present an in-depth study of the piezoresistive effect in carbon nanotube fibers, <i>i.e.</i>, yarnlike assemblies made purely of aligned carbon nanotubes, which are expected to find applications as electrical and electronic materials. The resistivity changes of carbon nanotube fibers were measured on initial loading, through the elastic/plastic transition, on cyclic loading and on stress relaxation. The various regimes of stress/strain behavior were modeled using a standard linear solid model, which was ...