"If the plans are given the green light by the SGSA and their local Safety Advisory Group amongst others the Oteley Road ground will become the first all-seater stadium in England and Wales to introduce safe standing," the club said in a statement.
Shrewsbury are hoping to follow Scottish side Celtic, who introduced a 2,900-capacity safe standing section last year.
"There's a clear demand from our fans for an area where they can stand safely," said Roger Groves, the joint chairman of Shrewsbury Town's Supporters Parliament.
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"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."
All-seater stadiums became mandatory in England's top two divisions following the Hillsborough disaster in 1989 when 96 fans were killed in a crush at the FA Cup semi-final between Liverpool and Nottingham Forest.
However, West Bromwich Albion said last week they were willing to take part in a safe standing pilot scheme at the Hawthorns as proposed by the Premier League.
(Reporting by Hardik Vyas in Bengaluru)
