Simpson has found himself on the 60-day injury list after having surgery to repair the ulnar nerve in his left elbow, and he is not expected back in the lineup until at least the middle of July.
Hurt has been sent to the 60-day injured list with right shoulder inflammation, and he is not expected to be activated until at least the beginning of June.
Kershaw is expected to remain on the 60-day injured list until at least the end of July while he recovers from surgery to repair the gleno-humeral ligaments and capsule in his left shoulder.
May has been shuttled to the 60-day injured list after having surgery to repair his flexor and UCL in his right elbow, and he is not likely to suit up until the end of July.