If the biomechanic function of the different anatomical sub-structures of the knee joint was needed in physiological conditions, the only possible way is a modelling approach. Subject-specific geometries and kinematic data, acquired from the same living subject, were the foundations of the 3D quasi-static knee model developed. Each cruciate ligament was modelled by means of 25 elastic springs, paying attention to the anatomical twisting of the fibres. The sensitivity of the model to the cross-sectional area was performed during the anterior/posterior tibial translations, the sensitivity to all the cruciate ligaments parameters was performed during the internal/external rotations. The model reproduced very well the mechanical behaviour reported in literature during anterior/posterior translations, in particular considering 30% of the mean insertional area. During the internal/external tibial rotations, similar behaviour of the axial torques was obtained in the three sensitivity analyses. The overlapping of the ligaments was assessed at about 25 degrees of internal axial rotation. The presented model featured a good level of accuracy in combination with a low computational weight, and it could provide an in vivo estimation of the role of the cruciate ligaments during the execution of daily living activities.