UPDATE: The council has said that anyone already queuing before 10pm will be able to cast their vote as the polling stations will remain open to accommodate them.
Caerdydd council is advising voters to allow "plenty of time" to vote due to "very busy" polling stations.
There are reports of long waiting times outside polling stations across the city.
Long waiting times have been reported in Treganna, in the Gorllewin Caerdydd constituency, which is currently held by First Minister Mark Drakeford. Long queues have formed outside Broad Street polling station.
Polling stations in Yr Eglwys Newydd (Gogledd Caerdydd), and in Cyncoed (Caerdydd Canolog) are also reported to be busy.
The council said that it is ensuring that Covid-19 safety measures are being followed, despite the long queues.
Some voters have expressed fears that they might miss out on voting as a result of the waiting times.
In response to the council's message, Vanessa Oldham said: "It’s an hour and a half queue at our local polling station in canton. Think people are going to miss out on voting because of it."