It is three weeks since the 21-year-old was first reported missing and, in a statement released on Thursday, Lisa and Russ Squire said: "In that time we haven't been able to speak to her and we haven't been able to hug her.
"We haven't been able to tell her we love her, or hear that she loves us.
"She went out to have fun with her beloved friends.
"Since then it has been a time of unending torture for her friends and family, but we all have unending hope that she will be found."
Libby went missing on February 1 after a night out in Hull, where she is studying at the city's university. She was seen near her student house but never made it home.