In a select system for an automatic transmission in which switchover between a mechanical automatic mode and an electrical manual mode is achieved by a lateral shift of a select lever, the select lever has an engaging protrusion extending a distance to one side, which remains inserted in an engaging groove opened in a rotatable linkage member. The diameter of the solid core, the center hardness, surface hardness and hardness difference between the center and surface of the solid core, the thickness and surface hardness of the envelope layer, and the thickness and surface hardness of the intermediate layer are each optimized within specific ranges. The improved arrangement is especially suitable for a rear wheel suspension in a motor vehicle, thereby permitting a high degree of longitudinal softness and high windup strength.