Question: Can a Muslim do modeling for a living?
What a Muslim cannot do is to open his/her private parts for strangers.
The private parts for men are between his belly and his knees. The private parts for women to the opposite sex consist of her whole body except her face, her hands and her feet. Her private parts to the same sex are between her belly and her knees.
Consequently, a Muslim can do modeling as long as he/she guards his/her private parts from seeing by other people.