A computer-based model of the knee was used to study forces in the cruciate ligaments induced by co-contraction of the extensor and flexor muscles, in the absence of external loads. Ligament forces are required whenever the components of the muscle forces parallel to the tibial plateau do not balance. When the extending effect of quadriceps exactly balances the flexing effect of hamstrings, the horizontal components of the two muscle forces also balance only at the critical flexion angle of 22 degrees. The calculations show that co-contraction of the quadriceps and hamstring muscles loads the anterior cruciate ligament from full extension to 22 degrees of flexion and loads the posterior cruciate at higher flexion angles. In these two regions of flexion, the forward pull of the patellar tendon on the tibia is, respectively, greater than or less than the backward pull of hamstrings. Simultaneous quadriceps and gastrocnemius contraction loads the anterior cruciate over the entire flexion range. Simultaneous contraction of all three muscle groups can unload the cruciate ligaments entirely at flexion angles above 22 degrees. These results may help the design of rational regimes of rehabilitation after ligament injury or repair.