Captain Robbie Keane, 32, has been selected despite missing his last three Major League Soccer games for club Los Angeles Galaxy with an ankle injury.
There were returns for Spartak Moscow midfielder Aiden McGeady and Norwich forward Anthony Pilkington but Wolves striker Kevin Doyle was left out after suffering relegation again with his club while Ciaran Clark of Aston Villa is out injured.
Ireland take on England at Wembley on May 29 before the friendly with Georgia at the Aviva Stadium on June 2.
Trapattoni's men then host the Faroe Islanders on June 7 in Dublin in a Group C qualifying fixture before the final pre-summer match, another friendly, against the world and European champions Spain at New York's Yankee Stadium on June 11.
The Italian said: "We must consider the positives from our games against Sweden and Austria when preparing for these fixtures.
"We produced two strong performances and the players have proven that they are working very well together.
"I am very happy to have the squad together for these games, firstly to prepare for the Faroe Islands World Cup qualifier, and then for the challenges we have ahead of us in September.
"This trip creates the chance to work with the players for a longer period than usual in order to bond and plan for the remainder of our FIFA World Cup qualifier games.
"These matches will provide me with the opportunity to experiment with different players and tactics. I am looking forward to assembling the squad in London on May 26."
The Football Association of Ireland says it will trim the squad next week to accommodate any injuries suffered in the final round of Premier League games.
Ireland currently sit fourth in their group behind Germany, Sweden and Austria and have not won a competitive match since beating the Faroes 4-1 in October after the 6-1 home thumping from the Germans.
Republic of Ireland squad: David Forde (Millwall), Keiren Westwood (Sunderland), Darren Randolph (Motherwell), John O'Shea (Sunderland), Sean St Ledger (Leicester), Damien Delaney (Crystal Palace), Richard Keogh (Derby), Marc Wilson (Stoke), Seamus Coleman (Everton), Stephen Kelly (Reading), Darren O'Dea (Toronto), Paul McShane (Hull), Glenn Whelan (Stoke), James McCarthy (Wigan), Paul Green(Leeds), Jeff Hendrick (Derby), Aiden McGeady (Spartak Moscow), Anthony Pilkington (Norwich), James McClean (Sunderland), Robbie Brady, David Meyler (both Hull), Andy Keogh (Millwall), Robbie Keane (Los Angeles Galaxy), Shane Long (West Brom), Conor Sammon (Derby), Jon Walters (Stoke), Simon Cox (Nottingham Forest), Wes Hoolahan (Norwich).