Both players miss out on England's Webb Ellis Trophy defence in France next month, while Nick Abendanon, Danny Cipriani, Toby Flood, Kevin Yates, Tom Palmer and James Haskell have also failed to make it.
Gloucester centre Tindall, a 2003 World Cup winner, has been battling to recover from a broken leg suffered last April, while Sale Sharks fly-half Hodgson last played almost nine months ago due to a serious knee injury.
Ashton's group is largely as expected, with Perpignan prop Perry Freshwater shading Yates for a front-row berth in a squad that will be captained by Wasps tighthead Phil Vickery.
Centre Mike Catt, 36 next month, will equal Jason Leonard's England record of featuring in four World Cup tournaments, while 35-year-old Wasps back-row star Lawrence Dallaglio has also been selected.
There are 12 survivors from England's original 2003 World Cup squad, plus Wasps lock Simon Shaw, who travelled to Australia four years ago as a replacement but did not play.
Ashton put the finishing touches to his squad on Sunday following England's 21-15 tournament warm-up defeat against France at Twickenham.
The announcement culminates an intensive seven-week training programme that has seen England work with the Royal Marines and work in baking temperatures on the Algarve.
Some of his final decisions would have been marginal calls, with Newcastle back Flood especially unlucky, but there is joy for ex-Great Britain rugby league captain Andy Farrell, who has been named after making just four Test appearances.
Farrell has been widely criticised for his lack of pace in the union game, yet he offers considerable leadership qualities and the mental toughness Ashton has looked for in arriving at his final 30.
The same can be said for 79 times-capped Dallaglio, whose presence in the squad and influence on it will prove considerable.
The survivors from 2003 are Dallaglio, Vickery, Catt, Jason Robinson, Josh Lewsey, Jonny Wilkinson, Andy Gomarsall, Mark Regan, Martin Corry, Ben Kay, Lewis Moody and Joe Worsley.
Ashton spoke to all of the players who did not feature in his final plans on Sunday.