A mathematical (computer) model was developed and used to study the mechanics of the human knee during extension exercises employing an isokinetic dynamometer. All parts of the body were fixed to ground, except for the right shank and foot, which were free to move in the parasagittal plane. A linkage attached the dynamometer to the shank; tibiofemoral articulation consisted of single-point contact, allowing both sliding and rolling to occur. Physiologically based representations of ligaments and muscles imparted forces to the shank. A forward dynamics simulation was performed to calculate the forces developed in the knee for isokinetic speeds ranging from 0 (isometric exercise) to 300 degrees /s. Simulations were conducted for a constant-speed phase during isokinetic knee extension exercise. It was assumed for the duration of each simulated exercise that the quadriceps were fully activated and the other muscles were fully deactivated. The force in the anterior cruciate ligament was found to be governed by the force-velocity properties of the quadriceps; the model predicts that 300 deg/sec isokinetic exercise can reduce the force transmitted to the ACL by almost a factor of two compared with that present during isometric knee extension.