Computer Pornography and Child Exploitation Prevention Act of 1985 - Amends the Federal criminal code with regard to the importation or transportation of obscene material. Makes it a Federal offense to enter, store, or transmit any obscene, lewd, or lascivious writing, description, or picture.

Prohibits any person from knowingly entering or transmitting by means of a computer, or publishing or reproducing by other means, any notice, or advertisement, or any minor's name or other identifying information for purposes of: (1) encouraging sexually explicit conduct (or the visual depiction of such conduct) with any minor; or (2) disseminating any visual depiction if such conduct involves the use of a minor engaging in sexually explict conduct.