The Sky Bet League One side is aiming to create a safe standing area with a capacity of around 500 in the Salop Leisure Stand.
Shrewsbury's stadium, Greenhouse Meadow, was built 10 years ago and is one of 29 in the Football League which can currently apply for safe standing.
Clubs in England's top two divisions have been legally required to have all-seater grounds since the measure was recommended by the 1990 Taylor Report into the Hillsborough disaster.
Should Shrewsbury win approval from the Sports Ground Safety Authority, then they would become the first all-seater stadium in England and Wales to introduce safe standing.
"There's a clear demand from our fans for an area where they can stand safely," Roger Groves, the joint-chairman of the club's Supporters' Parliament, told the Shrewsbury website.
"We see that at every game with several hundred choosing to stand at their seats, which is not altogether safe.
"Rail seats will ensure that nobody falls over no matter how wildly they celebrate a goal and, by having a dedicated standing area, we believe that the overall atmosphere in the stadium will also be enhanced."
The Premier League recently wrote to its 20 clubs asking if they would be interested in taking part in a trial to reintroduce standing sections in their grounds.
Ladbrokes Premiership champions Celtic installed 2,600 rail seats - seats that can be flipped down or locked into an upright position, with safety barriers separating each row - at Parkhead last season and it was considered a major success.
"As a Scot, I am very familiar with the great success that Celtic have had with their rail seating section," said Shrewsbury chief executive Brian Caldwell.
"So when the Supporters' Parliament approached me about introducing the same concept here, I was immediately keen on the idea.
"Our safety officer has also visited Celtic Park recently and is all for it."
Shrewsbury plan to replicate Celtic's method and are raising the funds required through a crowdfunding campaign.
"We see it as an enhancement in spectator safety and a welcome provision of supporter choice," added Caldwell.
"We hope, too, that by pioneering the use of rail seating in the EFL, we will be playing a useful part in paving the way for other clubs in England and Wales to follow suit in due course."