Thornton, who play in the Halifax League Premier Division, will visit Whinney Lane for the first time.
In the first round, Streethouse defeated Houghton Main, Fairburn knocked out Clayton West and Carlton beat Ackworth.
The final of the national competition is at Lord’s on Sunday, September 4.
Streethouse are holding a race night on Saturday, May 21, in the clubhouse (8.45pm).
Proceeds will go to McMillan Cancer Support Group.
The club are looking for sponsors for the races and raffle prizes.
Anyone who can help should contact club secretary Stewart Simpson on 07908231370 or e-mail:[email protected]
Streethouse will be holding a club open day this to promote cricket in the area on Thursday, August 18.
Any children between the ages of eight and 15 wishing to attend the event should contact Stewart Simpson.
The event will involve all children taking part in learning to play cricket on the day and then playing a game of quick cricket.