Fans invaded the pitch at Hampden following Hibernian’s historic victory over Rangers in the Scottish Cup final.
The Edinburgh side beat the Ibrox club 3-2 with a late goal in injury time.
Hibs fans spilled onto the park after the full-time whistle. Rangers fans followed and mounted police were deployed to keep both sets of supporters apart.
Rangers said some of their players were assaulted. The SFA said a full investigation would be carried out.
A late header from David Gray saw Hibernian end their 114-year wait to lift the Scottish Cup.
Anthony Stokes scored twice for Hibs, with Rangers goals from Kenny Miller and Andy Halliday.
Scottish Football Association chief executive Stewart Regan said the SFA was “appalled by the scenes of disorder and the contemptible behaviour” following the cup final.
“What should have been an historic, memorable Scottish Cup final will now, sadly, be remembered for all the wrong reasons,” he said.
“Police Scotland and the stadium management initiated a Crisis Liaison Group as soon as the disorder began and we thank them for containing the situation as quickly as possible.
“The Scottish FA, along with Police Scotland and the stadium management have initiated a full investigation into the scenes that unfolded to understand how such a volume of supporters were able to enter the field.”
Rangers said some of their players and staff had been assaulted by Hibs fans as they tried to leave the pitch. The team received their runners-up medals in the dressing room.
As Hibs fans returned to the stands part of the pitch was ripped up and the goal posts were broken by people climbing on them.
The invasion delayed the presentation of the trophy and there was no lap of honour by the Hibernian players.
A statement from Rangers condemned the “disgraceful behaviour of Hibs fans”.
A spokesman said: “Rangers players and staff were assaulted by these fans who invaded the pitch and in the interests of their safety could not return to the pitch for the medal presentation.
“There can be no place for the violent behaviour witnessed at the end of the final and Rangers fully expect the Scottish Football Association and Police Scotland to launch an investigation to find out where security measures failed.
“The club would like to commend Rangers fans for the restraint they showed under severe provocation.”
Police horses were last needed at the 1980 Scottish Cup final between Celtic and Rangers.
Source:: BBC UK