The force-strain relation and tensile strength of carbon nanotube bundles are studied based on the assumption that the tensile strength of individual carbon nanotubes (CNTs) obeys the Weibull distribution, with nonlinear stress-strain behavior. The Weibull modulus of the CNT that characterizes the dispersion of tensile strength can be estimated in terms of the maximum sustained force and the failure strain of the bundle. Bundles of single-walled carbon nanotubes (SWNTs) were subjected to tensile testing using a nanomechanical testing device. Results show that the nonlinear behavior of SWNTs does affect the force-strain relation of SWNT bundles, more apparent at large strain.