May and Wood are both named on the bench with the rest of the side unchanged after Saturday's opening 19-16 victory over France at Twickenham.
Jones, having lured Wales into thinking the game would be played in the conditions they favour, changed tack and announced shortly before the deadline that England wanted the roof to remain open.
"Playing Wales in Cardiff is one of the biggest games in world rugby and we're excited".
Wales defence coach Shaun Edwards suggested that Faletau is likely to play off the bench.
It's hard to escape in the modern game; results are often decided by the back rows. You do the fundamentals of the game well and you win the game of rugby.
"Nathan and Jack have been around the team for a long time too â- Jack went on tour (to Australia) in the summer with us, so he has done his time", he added when speaking at England's training base in Bagshot, southwest of London.
15-Mike Brown, 14-Jack Nowell, 13-Jonathan Joseph, 12-Owen Farrell, 11-Elliot Daly, 10-George Ford, 9-Ben Youngs; 8-Nathan Hughes, 7-Jack Clifford, 6-Maro Itoje, 5-Courtney Lawes, 4-Joe Launchbury, 3-Dan Cole, 2-Dylan Hartley (captain), 1-Joe Marler. Wood, who has recovered from a shoulder injury, has 46 caps while Clifford, Itoje and Hughes have only four back-row starts between them. "Hopefully we can do the occasion justice", said Wales captain Alun Wyn Jones.
England won 21-16 on their last visit to Cardiff, but they have have recorded just two wins in the last seven matches at the Millennium Stadium. We are just waiting to see what they (England) say.
England's replacements, or "finishers" as Jones now terms them, made a huge impact against France, and one of them in Nowell gets his chance from the start this week.
England are now enjoying a 15-match winning streak under coach Eddie Jones after their narrow win over France at Twickenham during the Six Nations.
"They're two vital players for us. Every game is important and our supporters, and Wales is our next game so its most important".
"We now have a platform to work from in this competition, however we have been fully focused this week on how we can improve against Wales on Friday".
At Quins he has experienced the frustration of waiting for a starting place, with Chris Robshaw a club-mate and England back-row rival.
"We are just making sure that whatever happens, we are ready for kick-off tomorrow". "We want to go out this week and redeem ourselves". We watched the England game (against France) live.
If Cuthbert plays, it will be his first Six Nations appearance since he featured in Wales's 25-21 defeat by Grand Slam champions England at Twickenham a year ago.