A model has been developed to definitively characterize the resistance properties and the joint loading (i.e., shear and compressive components of the joint reaction force) in single-joint exercises with ideal elastic bands. The model accounts for the relevant geometric and elastic properties of the band, the band pre-stretching, and the relative positioning among the joint center of rotation and the fixation points of the band. All the possible elastic torque profiles of ascending-descending, descending, or ascending type were disclosed in relation to the different ranges of joint angles. From these results the elastic resistance setting that best reproduces the average-user's knee extensor torque in maximal isometric/isokinetic efforts was determined. In this optimized setting, the shear tibiofemoral reaction force corresponding to an anterior (posterior) tibial displacement was 65% smaller than (nearly the same as) that obtained in a cam-equipped leg-extension equipment for equal values of resistance torque peak, whereas the compressive tibiofemoral reaction force was 22% higher. Compared to a weight-stack leg-extension equipment, an elastic resistance optimized setting has the potential to give a more effective quadriceps activation across the range of motion, and greatly reduces the anterior cruciate ligament strain force, which represents the main drawback of existing open kinetic-chain knee-extension exercises.