Police negotiators and armed police are at the scene at a block of flats, thought to be Nathan Court, on Scalby Road.
People were urged to stay away from the area while officers deal with the incident.
Scalby Road is closed between the junction with Falsgrave, at the Crown Tavern, and Manor Road roundabout.
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North Yorkshire Police said: "Please avoid the area around Scalby Road (near Falsgrave Road), in Scarborough.
"Roads are closed in the area to keep the public safe while specially-trained police negotiators work to resolve the incident.
"Please help us by staying away from the scene."
Nathan Court is a flats development on Scalby Road near its junction with Harley Street, and opposite the junction with Stepney Avenue.