A constitutive model is proposed for the description of the tensile properties of medial collateral ligaments (MCLs). The model can reproduce the three regions -- the toe region, the linear region, and the failure region -- of the stress-stretch curve of ligamentous tissues. The collagen fibers are assumed to be the only load-bearing component of the tissues. They are all oriented along the physiological loading direction of the ligament. They are crimped in the slack configuration and are unable to sustain load. After becoming taut and before failing, each collagen fiber exhibits a linear elastic behavior. The fiber straightening and failure processes are defined stochastically by means of Weibull distributions. Published experimental data for the MCLs are employed to validate the constitutive relationship. Finally, the constitutive model is generalized in order to describe the three-dimensional mechanical behavior of the ligaments by following he structural approach.