Red Sox starter Josh Beckett is in Cleveland today getting his right thumb examined by Dr. Thomas Graham, a hand specialist, according to multiple reports.

Ken Rosenthal of Fox Sports was the first to report the Beckett visit to see Dr. Graham at the Cleveland Clinic. According to Rosenthal:

The team wants Beckett to visit Graham for “peace of mind” and still expects him to pitch the second game of the season, sources say. But the visit will mark the second time in two days that Beckett has seen a hand specialist for a thumb problem.

Beckett was in San Antonio on Monday to be examined by Dr. Mark Bagg, another hand specialist.

“If he needed to talk to me, he was going to talk to me. He didn’t talk to me, so I think he was fine,’’ Red Sox manager Bobby Valentine said Monday regarding Beckett.

Beckett threw a lengthy bullpen session on Sunday and did not miss any of his starts this spring. He allowed two earned runs on seven hits over 19 innings against major league competition.

“He threw 100 pitches yesterday and felt great, hit location,’’ Valentine said. “He’s had a little situation that he’s getting taken care of today just for peace of mind.

Red Sox reliever Andrew Bailey is also having his right thumb checked out by Dr. Graham in Cleveland today as well.

The Globe reported Monday that Red Sox team doctors in Boston determined Bailey will require surgery. If Graham agrees with the recommendation for surgery, it could happen as soon as today.

Graham also performed surgery on Kevin Youkilis and Jarrod Saltalamacchia in 2010. Youkilis had a torn muscle in his right thumb and Saltalamacchia a torn ligament in his left thumb.