Grossman arrived at training camp on Tuesday. He said he signed a one-year deal because he "wanted to see how this year played out."
Grossman was an unrestricted free agent, but he indicated he didn't seriously consider any team other than the Redskins.
Beck has been inconsistent so far, not surprising given the lack of offseason practices.
"His arm was a little sore today," Shanahan said Tuesday. "I could see it. He didn't quite have the zip on it that he normally has."
Grossman can't practice until Thursday under the league's post-lockout rules.
He started the final three games last season after Donovan McNabb was benched.
Tatupu, who was granted his release when he declined to take a pay cut, was visiting with the Oakland Raiders Tuesday.
Information from The Associated Press was used in this report.