Along with all-rounder Stokes, England are also missing opener Zak Crawley, who broke a finger on the final day of the 3-0 series win against West Indies last month.
In their absence, Dan Lawrence will open the batting and Matthew Potts has been named as an extra seamer. Harry Brook steps up as Pope’s vice-captain.
England’s last Test at Old Trafford, against Australia last summer, was ruined by rain, ending the home side’s chances of regaining the Ashes. The forecast this week is mixed for Sri Lanka’s first Test in this country in eight years.
“I’ve not looked too closely at the weather because if it rains, it rains, but it’s not going to change the way we necessarily go about it,” said Pope.
“A 3-0 win is always the target. If we can keep playing our best cricket, like we have, then hopefully we can look back in three or four weeks and that’s the end result.
“They would have watched us, and how we’ve played in the West Indies, and they will be ready to throw some punches themselves. If we can play our best cricket, hopefully we can get that 3-0.”