Here are some synonyms:
* Buried in a book
* Lost in a book
* Devoured the book
* Engrossed in reading
For example:
* "The little girl was so stuck into her book that she didn't even notice her mom walk in."
* "He stuck his nose into a book and was gone for the rest of the afternoon."
The phrase is often used to describe someone who loves to read and finds it difficult to put a book down once they start reading.