It was one of two tower blocks in the area designed by Sir Basil Spence and contruction took place between 1963 and 1965 after being approved in 1960. It was opened by Queen Elizabeth in person. Its striking brutalist design was inspired by Glasgow's shipbuilding heritage. Spence said at the time that when people were hanging out their washing on the balconies, the tower block would look like a vast sailing ship.
The flats however, were very poorly built by the HHC and damp and structural problems plagued the tower throughout its short life. Crime was an issue in the days before concierge policing and CCTV with cases of brutal assualts and muggings in the stairwells.
16-32 Queen Elizabeth Square was demolished in 1993 along with its sister block 2 Queen Elizabeth Square. The experiment, a failure. A large crowd had gathered to watch what was the fourth high rise demolition in Glasgow and unfortunately an old woman died after being hit by debris from the falling structure. Queen Elizabeth Square was demolished completely by 1995 when the low rise 4 storey blocks were demolished and the area became a wasteland for nearly a decade before another new and exciting housing experiment was built on the land involving medium rise private flats built as part of Gorbals regeneration.