The calls for a month of free parking are being made by the mayor of Bridgnorth and representatives of the area on Shropshire Council.
The cohort say all car parks owned by Shropshire Council in the county's market towns should be made free when non-essential shops reopen from April 12.
Supporting the calls are Bridgnorth's four representatives on Shropshire Council, Elliott Lynch, Les Winwood, Christian Lea and William Parr, as well as the town's mayor Councillor Kirstie Hurst-Knight.
Also in support are Much Wenlock's Shropshire Councillor David Turner, Councillor Robert Tindall, who represents Brown Clee, Councillor Michael Wood, who represents Worfield and Councillor Tina Woodward, who represents Alveley & Claverley.
A joint statement issued by the group said: "We recognise just how important it is to local businesses in Bridgnorth that free parking in Shropshire Council-owned car parks is made available from April 12 onwards.
"Bridgnorth has a fantastic selection of independent shops which deserve to be supported. As we emerge out of lockdown, any assistance that can be offered to make Bridgnorth town centre a vibrant place to shop once again will be very much welcomed by retailers.
"We also recognise how this would benefit all traders in Shropshire and therefore extend this call to all market towns throughout the county."
Candidates at the upcoming Shropshire Council elections in May, Tim Harris and Richard Marshall, have also issued their support for the scheme.
Shropshire Council made its car parks free at 11am for six weeks from December last year to give shops, pubs and cafes a welcome festive boost.
Councillor Lea, who represents Bridgnorth East & Astley Abbotts, added: "Councillors believe that it is essential that Shropshire Council makes free parking available in Bridgnorth to offer support to local traders when they reopen their doors, after having been closed for over three months.
"Retailers have had a particularly tough time over the course of the past year, having been closed for the duration of the three lockdowns due to the coronavirus pandemic."
Councillor Lea said the idea had been proposed to the leader of Shropshire Council, Peter Nutting, who said the request would be considered.