The funeral service was held at the Slavic Christian Church in Tacoma, with an interpreter translating parts of the service from Russian.
Zina was abducted from an alley outside her home on July 4th, then found dead near Eatonville in rural southern Pierce County on Thursday.
Terapon Adhahn, a 42-year-old convicted sex offender from Thailand, is being held as a person of interest in the case and is expected to be charged in her death.
During the service, Katie Thaut, one of Zina's teachers, told of the list of 10 memories she had made with Zina's sisters.
She said at the top of the list was Zina's love of her family and Jesus.
"Her sister said Zina's idea of a fun party would be to go swimming in the summer," she said. "She was my favorite student."
Among the mourners were police officers and FBI agents who had participated in the search for Zina.
"Sometimes these stars become very heavy, and I can't think of another time that they've felt the heaviest," Tacoma Police Chief Don Ramsdell said.
The Linnik family came to the United States 10 years ago from the Ukraine.