The Patriots already were trying to plug gaps on the offensive line after allowing 38 sacks in 2015, and Solder has been a steady presence over the past six years. Cooper came to New England in a trade for linebacker Chandler Jones and suffered a foot injury early in camp.
The Patriots released center Bryan Stork and placed right tackle Sebastian Vollmer on the physically unable to perform list at the end of camp. David Andrews, in his second year, is expected to start at center, while Marcus Cannon (eight starts in 2015) moved into the starting lineup at tackle.
Tom Brady also will miss the opener as he begins his four-game suspension for his role in Deflategate.