Morgan McVicarr said her father had got off the ride moments before the accident. She wrote on Twitter: "Can't believe there's been an accident at m&ds, just after brogan and my dad got off the ride hopefully everyone involved is safe!!"
Katie Burns said she had just finished riding the rollercoaster and was walking past when the carriage crashed with children on board.
On Facebook, she said: "Literally got off the Tsunami at M&Ds and then walking past and the next lot of people get on and the full thing goes off the tracks.
"Honestly never been so scared in my life... Kids and adults are still on it upside down, it's like something out a horror film, children crying and everything.
"Literally can't believe this, my heart goes out to everyone on it, a full load came off the track ... and on the pavement, like a horror film worse thing ever heard and seen, can't get over this."
James Millerick, from Glasgow, who is thought to have been at the park with his girlfriend when the incident occurred, wrote that he was "absolutely horrified" by the crash.
Mr Millerick had been queuing for another rollercoaster when he heard "shrieks" from customers. He believes the ride slipped off the tracks as it came round a corner and said he thought it did not fall from the highest point.
He told Sky News: "When we got there the rollercoaster had come off the track entirely - straight through the gated fence at the side of the rollercoaster and was upside down on the concrete path at the side.
"There were maybe seven or eight individuals, mostly of younger age between maybe 10 and 15 years old that were actually trapped inside the rollercoaster lying on the ground. The harnesses were still on as well so there was absolutely no movement."
Steven Harvey, whose friends were at the park, warned people to stay away while emergency services were at the scene. He wrote: "Guys stay away from MDs one of the rides have come off the rails and gone into the crowd. People in it and trapped underneath."
Hundreds of users were quick to send their best wishes to those still trapped. Ruth Davidson, leader of the Scottish Conservative Party, tweeted: "Awful news coming from M&Ds. Deeply concerning - our thoughts are with those affected and with emergency responders."
First Minister of Scotland Nicola Sturgeon said: "My thoughts are with everyone involved in this terrible incident at M&D's theme park, especially those injured."
A spokesman for M&D's confirmed the theme park was now closed. They added: "A serious incident occurred at M&D's today involving the tsunami rollercoaster. We have all emergency services on site to assist. The theme park is closed until further notice."
Police Scotland said it was unable to give more details about the victims' injuries. They added: "At this time, we are aware of 11 casualties - two adults and nine children, who are all being treated at local hospitals."
The Scottish Ambulance Service said six ambulances, a special operations team and emergency doctors were sent to the park.
Tsunami is Scotland's only inverted rollercoaster. It reaches speeds of up to 40mph (64km/h) and includes corkscrew twists and loops.
Children under 10 are prohibited from riding the Tsunami and a minimum height restriction of 1.4m applies.
In 2011, nine people were rescued from the same ride after being trapped for eight hours.
