They beat Hinckley 2-0 in front of a large crowd at Welford Road before Leicester Tigers Guinness Premiership game with Newcastle Falcons on Saturday.
Wymondham have been joined in the last four by Lutterworth, who knocked out holders Nottingham Boots Corsairs.
Their quarter-final ended in a 1-1 draw but three-time Lutterworth went through by virtue of having scored the first try of the game.
Wymondham and Lutterworth join Burton and Stratford in the semi-finals, who won through at an earlier date.
The semi-finals will be played at Welford Road before Tigers'Guinness Premiership game against Worcester Warriors on Saturday, February 21.
Scott Clarke, Tigers community manager, said: Congratulations to all of the players for their part in two fantastic games of rugby.
They were played in great spirit, and the youngsters displayed a lot of skill in what were difficult conditions.
The Prima Tiger Cup, which is supported by Loughborough-based Prima Solutions, is now in its 15th season and is open to under-10s teams from across the country.
More than 50 sides entered this year's competition, which began with local festivals at Stoke RFC in Staffordshire, Kenilworth RFC in Warwickshire, Swaffham RFC in Norfolk, Nottingham Boots Corsairs RFC and at Market Harborough RFC in Leicestershire.
More information on the Prima Tiger Cup is available from Leicester Tigers on 08701 28 34 30, or by clicking here.
