Boss Sam Ricketts goes head-to-head with his former side, led by Nuno Espirito Santo, who sent Liverpool packing in the previous round.
The clubs are separated by 30 miles and 53 places in the league tables. They last met in this competition in the 1978/79 season, where a quarter-final – Town’s best ever effort – went to a Gay Meadow reply under player-manager Graham Turner, who later became Wolves boss.
Beckles, 27, and the current crop of Town players know they can achieve a fairly rare feat by overturning the odds against Wolves’ Premier League all-stars.
Shrewsbury have gone beyond the fourth round just twice in 35 years. They have only reached the fourth round four times in three decades.
For Ricketts and Town, this is a welcome break from the pressure of League One football, where Salop are working to move themselves away from the drop zone.
But there is still pressure. There is no expectancy, but a pressure to perform and give a good account of themselves on the grand occasion.
“For me and the lads it’s probably not sunk in as of yet because we really want to be focusing on the league,” said Beckles, who himself has FA Cup previous.
“I know a lot of the boys have had good experiences in the FA Cup and the potential of another giant-killing would be one to cherish.
“I know it would mean a lot to the fans. We want to win it. It’ll build momentum that we can take into the league.”
Defender Beckles’ FA Cup pedigree goes even further back than last season’s third-round replay at West Ham’s London Stadium.
Two years ago, Beckles scored the winner against Luton to send Accrington Stanley into the fourth round for just the second time in their history (almost 50 years after the first). “At Accrington I scored the winner against Luton for the fourth round. That was a big deal,” he added.
“I look back and see we made a bit of history. To know that (Town’s record) is something we’ll hold to and remind the lads.”
“Some of us have been around enough and played against big-name players.
“It’s always good to push yourselves against them, we did it against Stoke. It’s another scalp, and confidence boost for some of the young lads as well