It is believed the woman was trying to get out of the lift at Rodgers Towers in Maryhill after it became stuck between the eighth and ninth floors. The 32-year-old was taken to hospital but died a short time later.
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The Health and Safety Executive has launched an inquiry. A report has been sent to the procurator fiscal.
Cube Chief executive, Lynn McCulloch said: "We are shocked and saddened by this tragic incident and our sympathies go out to the family of the person who died.
"Our staff are now working with the police and health and safety personnel to try to ascertain how this accident occurred. While we have a very thorough lift maintenance programme in place, we have instigated an immediate inspection of all lifts in the Wyndford Estate."
Strathclyde Police said the woman died after falling nine floors down the shaft at Wynford Road. A spokeswoman said the incident took place at about 0035 BST.
"The woman received serious injuries and was removed to the Western Infirmary where she died a short time later," she said.
(GK/JM)
