About 45 members of the local group held a 'die-in' at Barclays Bank in Castle Street on Saturday morning.
Children and adults lay on the floor of the bank with placards spreading the group’s message against climate change, while mystified bankers and customers looked on.
The demonstration was planned to highlight the role the activists claim the banking sector has played in perpetuating the current climate crisis.
It was supported by leafleting outside the bank and in Pride Hill, where members asked the public to join in in a 'mass switch' to a more ethical bank.
Adam Shipp, spokesperson for Extinction Rebellion Shrewsbury, said: "As historic heatwaves scorch Europe and the Arctic melts faster than even scientists predicted, it’s clear that we are in a climate emergency.
"The world needs to switch to clean energy as quickly as possible, but Barclays is ignoring the science and increasing their investment in dirty fossil fuels. It’s madness."
According to the group, Barclays in the top European banker for fracking and coal, investing $85 billion in fossil fuels and $24 billion in expansion.
Jamie Russell, a Barclays customer from Shrewsbury, was among the protestors and pledged to cancel his account with the bank.
"I don’t normally spend my Saturday mornings lying on the floor of a bank, but drastic times call for drastic action," he said.
"I’m doing this to highlight how Barclays’ greed is killing us and the planet. If Barclays cares more about profits than my children’s future, then I refuse to keep giving them my hard-earned cash. I’m switching to a more ethical bank."
The bank protest is one of several actions Extinction Rebellion Shrewsbury has planned for 2019 after being part of a coalition of groups that successfully lobbied Shropshire Council to declare a climate emergency.
Since the Shrewsbury group was formed in December 2018, it has grown from ten people to over 700 members.
Mr Shipp added: "We hope that people in Shrewsbury who are worried about climate change will come and find us on Facebook and Twitter or come to one of our regular meetings.
"We’re a wide mix of people – young and old, and from all kinds of different backgrounds. The thing that unites us is our concern about the climate crisis and our belief that the government and corporations aren’t treating it like the emergency it is. We’re just ordinary Shrewsbury residents. But if we don’t act, who will?"