One of the town's main River Thames crossings will close from Monday until 30 May for strengthening, resurfacing and waterproofing.
One resident contacted the BBC to say she had changed hospitals for giving birth to avoid getting stuck in possible traffic.
Council deputy leader Tony Page denied the closure would be "a nightmare".
"There will be inconvenience, there will be traffic congestion, but the longer-term benefit will be substantial to Reading," he said.
"The alternative would be to not to do the works and have permanent lane closures and weight restrictions on the bridge, which would simply be unacceptable."
Extra and discounted bus services will be provided on a number of routes between Caversham and Reading town centre during the closure.
However, some residents have decided to make alternative arrangements.
Expectant Caversham mother Nathalie Scaife is due to give birth on 26 May.
"I've experienced the bad traffic that you can have round here for the last couple of years and I really don't like the thought of being stuck during the closure having to give birth at the side of the road," she said.
"We've decided to switch our hospital to Wallingford in the opposite direction in a bid to reduce the burden.
"There's very little control I have over the situation, which when you're having a baby, is the worst possible thing."
For more information on the closure, visit BBC Radio Berkshire's dedicated information page.
A two-week closure of Reading Bridge is "necessary" and has to be done, according to the borough council.