It follows concerns by some local residents that such trains could be an easy target for terrorists.
Nuclear waste trains currently travel through Lawrence Hill, Stapleton Road, St Werburgh's and Ashley Down.
Liberal Democrat Councillor Sue O'Donnell will ask city council leaders next month what evacuation plans are in place in the event of an emergency.
She said: "These trains were built to withstand accidents, but terrorism is a different matter.
"We should be questioning whether there is a need for them to pass through residential areas at all."
Earlier this year, Bristol West MP Stephen Williams wrote to Energy Minister Malcolm Wicks asking what security measures were in place on nuclear waste trains.
Mr Wicks replied that train security was already "adequately robust" and that if there were a threat, "appropriate action" would be taken.
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