The anterior cruciate ligament (ACL) is liable to a major injury that often results in a functional impairment requiring surgical reconstruction. The success of reconstruction depends on such factors as attachment positions, initial tension of ligament and surgical methods of fixation. The purpose of this study is to find isometric positions of the substitute during flexion/extension. The distance between selected attachments on the femur and tibia was computed from a set of measurements using a 6 degree-of-freedom magnetic sensor system. A three-dimensional knee model was constructed from CT images and was used to simulate length change during knee flexion/extension. This model was scaled for each subject. Twenty seven points on the tibia model and forty two points on the femur model were selected to calculate length change. This study determined the maximum and minimum distances to the tibial attachment during flexion/extension. The results showed that minimum length changes were $1.9{sim}5.8mm$ (average $3.6{pm}1.4mm$). The most isometric region was both the posterosuperior and anterior-diagonal areas from the over-the-top. The proposed method can be utilized and applied to an optimal reconstruction of ACL deficient knees.