A dramatic video of the incident has gone viral on Facebook, with it being shared over 40,000 times.
Officers were called to Spalton Road, Parkgate, following reports of a woman being held captive in a house.
They sealed off the street and armed officers surrounded the property.
A neighbour captured the siege on a mobile phone and streamed it live on Facebook.
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Officers could be heard negotiating with a man in the property and urging him to come out with his hands in the air.
One officer warned him that if there was any threat to life officers would shoot.
He could be heard saying: "Come to the door with your arms up and you will come to no harm.
"We are armed police officers and we will respond to whatever you do so don't do anything silly, do you understand?
"If you make any attempt to endanger life we will shoot to stop you."
Officers were also heard warning local residents to get back into their homes during the siege.
A woman was eventually let out of the property and was escorted away by police officers before a man came out and was led away in handcuffs.