Smith (elbow) has been throwing live batting practice sessions, Alex Pavlovic of NBC Sports Bay Area reports.
Smith is working his way back from Tommy John surgery which cost him the entirety of the 2017 season. He's expected to begin a rehab assignment in mid-April. He has been targeting a May 1 return and remains on track for that timeline. He's unlikely to be near the top of the closer depth chart when he returns, though with Mark Melancon already on the disabled list with a right elbow flexor strain, the Giants' bullpen situation is more fluid than it initially appeared.