Glasgow’s Barlinnie jail was operating at 139 per cent capacity in December and Inverness at 137 per cent.
Other sites at or exceeding their limit were Addiewell, Dumfries, Edinburgh, Glenochil, Kilmarnock, Perth and Shotts.
The figures were revealed following a parliamentary question from the Scottish Liberal Democrats, whose justice spokesman, Liam McArthur, warned that inmates are being “packed into prisons like sardines”.
At the start of 2018, five prisons were at or beyond their capacity, rising to nine out of 15 by the end of the year. Those operating within their capacity last month were Cornton Vale, Grampian, Greenock, Low Moss, Polmont and Castle Huntly.
McArthur said: “These new figures show that our prisons are bursting at the seams with the majority now full or overcrowded. People are being packed in like sardines.
“Those working in prisons have warned that the population surge is putting services at risk and jeopardising progress. Prison capacities are set for a reason. Staff need to work in a safe environment. Overcrowding makes it harder for them to work with individuals and help rehabilitate them.”
The Lib Dems said evidence shows short-term sentences are less effective at rehabilitating people than “robust” community-based sentences, which would reduce the pressure on jails.
McArthur said: “That is why the Scottish Government now must get on and introduce a presumption against short-term sentences of less than 12 months.”
A Scottish Government spokesman said: “Scotland has the highest rate of incarceration per 100,000 of population of any Western European country, which is why we are focused on action to stop people going to prison in the first place.”