Apparatus and methods for conditioning and pre-tensioning soft tissue grafts during joint repair surgery, such as during repair of the anterior cruciate ligament (ACL). The inventive apparatus is advantageously adapted and configured so as to enable a surgeon to independently apply a desired tensile load to individual graft strands or graft bundles of a multi-strand tissue graft. The inventive methods enable each graft strand or bundle to be properly tensioned so as to both “condition” the graft to prevent subsequent stretching, relaxation or elongation following surgery, which can destabilize the joint, and to pre-tension each graft strand or bundle to a predetermined amount so that each contributes to the strength and stability of the joint, thus resulting in a stronger and more durable joint. The tensioning device is advantageously equipped with structure for attachment to a patient's limb during the conditioning and pre-tensioning procedure. It has multiple adjustable tension applicators that can be independently manipulated so as to apply a separate tensile load to one or more ends of a tissue graft strand attached to each adjustable tension applicator.