ACL (Anterior Cruciate Ligament) has a fundamental role in knee biomechanics and ACL insufficiency is probably the most common knee pathology. Although widely investigated, ACL mathematical models are still controversial in simulations of knee kinematics. We have developed a new ACL model, made of 9 curvilinear independent fibers, corresponding to the individual surface fibers, which are described as a succession of 20 punctual physical particles linked by linear viscoelastic relations, and they can twist, bend and stretch under applied forces. The model has been validated on 4 fresh pig knees and has given very consistent results to describe ACL anatomy, function and mechanics. Simulations of passive kinematics give coherent results on fibers elongations, forces and ligament deformations, confirming the expected correlation between fibers' strain and stress. The advantage and the feature of this method with respect to previous models is the possibility to take into account more accurately ACL anatomy, mechanical properties and the ligament behaviour during range of motion. All input geometrical data, can be acquired in fixed position, respect sizes and shapes of the ligament, envisaging a possible application on human ACL to develop surgical planning and simulation.