If your vehicles transmission will not go into park then it could be caused by broken or binding shift linkage or even a stretched or broken transmission shifting cable depending on how your vehicles transmission is shifted.
Some vehicles have electronic shifting which happens through a solenoid which could be bad and not allowing the transmission to go into park like it should.
Another possible problem is that the parking gear in the transmission is bad or broken inside the transmission.
I would check the linkage for the shifting to the transmission to see if it's broken or binding up if it's the type of vehicle with that kind of shifting linkage.
I have a 92 Chevy Silverado pickup that sometimes will have hard time going back up into park and other gears after I drop it down to drive and I found out the linkage to the transmission was binding up.
I would have to shut the vehicle off and then reach underneath the vehicle and move the transmission linkage by hand underneath it and then it would go back into park just fine.
So check all that and if you still can't figure the problem out I would take the car to a transmission shop to have it checked out.
It's hard to say exactly what would be causing your cars transmission to not go into park unless I was there and looking at it.
But hopefully that will give you an idea on what could be causing it.