The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head-trunk-arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torque is the product of three variable functions of activation level, angular velocity dependence, and maximum isometric torque varying with joint angle. Simulations start from a balanced initial posture and end at jump takeoff. Jump height is maximized by finding the optimal combination of joint activation timings. Arm motion enhances jumping performance by increasing mass center height and vertical takeoff velocity. The former and latter contribute about 1/3 and 2/3 to the increased height, respectively. Durations in hip torque generation and ground contact period are lengthened by swinging the arms. Theories explaining the performance enhancement caused by arms are examined. The force transmission theory is questionable because shoulder joint force due to arm motion does not precisely reflect the change in vertical ground reaction force. The joint torque/work augmentation theory is acceptable only at the hips but not at the knees and ankles because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swings.