Staff at eight hospitals in the area – Morriston, Singleton, Neath Port Talbot, Cefn Coed, Gorseinon, Cimla, Tonna and Glanrhyd - say they have been underpaid for their work for many years.
Healthcare support workers on salary band 2 should only be providing personal care such as bathing and feeding patients, according to NHS guidance.
However, Unison says healthcare assistants employed by the Swansea Bay University Health Board are routinely undertaking clinical tasks such as monitoring blood, performing electrocardiogram tests and inserting cannulas.
The union says it is now going to talk to its members about what comes next, but warned that without an offer strikes look inevitable. In the ballot, 99% of staff who voted backed strike action.
Lianne Owen, Unison Cymru regional organiser, said: 'Healthcare support workers are some of the lowest paid staff in the NHS, yet they are routinely expected to carry out complex duties that they're not being paid for.
'Strike action is always a last resort, but board managers have to come back with an offer that compensates staff fairly for all the time they've been paid incorrectly.'
In response, a Swansea Bay University Health Board spokesman, said: ‘We're disappointed with the ballot for strike action over the banding of our healthcare support workers, an issue that is not unique to Swansea Bay or Wales for that matter.
'We respected their right to ballot and want to emphasise that we value all of our staff and the work they do – not least our healthcare support workers - and are committed to ensuring that everybody is treated fairly.'