Tensile strength distributions of multi-walled carbon nanotubes (MWNTs), single-walled carbon nanotube (SWNT) ropes and sub-bundles are studied by statistical approach based on the experimental data sets. It shows that the distributions can be adequately described by a two-parameter Weibull model. Considering further their nonlinear stress-strain behavior, the force-strain relation and tensile strength of SWNT bundles are studied. The Weibull modulus of the sub-bundles in a SWNT bundle can be estimated in terms of the maximum sustained force and the failure strain of the bundle. A SWNT bundle was subjected to tensile testing using a nano-mechanical testing device. The result suggests that the nonlinear behavior of SWNTs does affect the force-strain relation of SWNT bundles, mainly at large strain.