Season 1
In S1E5,
White Rabbit, we learn that Jack had gone to Sydney, Australia to try to find his missing father, Christian Shephard, a renowned Chief of Surgery. Jack was told by his mother that he had to bring his father home, after what Jack had done to Christian. Jack went to Australia and located Christian's hotel room. He was told by the hotel manager that his father hadn't been there in the past three days, and that he found it unlikely that any rental agent in Sydney would rent him a car. The manager also told Jack that Christian had been involved in an incident in the hotel's bar a few nights earlier and had to be escorted back to his room by hotel security. Jack finds bottles of alcohol and pills in his father's room, along with Christian's wallet.
Jack discovers his father's body in the morgue, where the medical examiner tells him that the body was discovered by the police in an alley in Queens Cross. Christian's blood alcohol content was high enough to have caused a myocardial infarction (a serious and fatal heart attack). Jack attempts to return his father's body to America for burial but is told by the airline desk agent that the body cannot be put on the plane without the proper documentation. Jack gives an impassioned speech to the agent about how he must get the body onto the plane because he has to land at LAX in 16 hours, to meet a hearse at the airport waiting to take his father's body to the cemetery for burial.
On the island, Jack had been searching the jungle thoughout the day and night for the vision of his father that he had been seeing. While at a campfire, he heard the sound of ice cubes rattling in a glass and went to investigate the noise. Jack discovered the caves, and inside, the coffin from the plane containing his father's body. When Jack opened the casket, he discovered that it was empty, and smashed the coffin to pieces with a pipe in a rage.
Season 3
In S3E1,
Tale of Two Cities, while being held captive in the Hydra station, Jack is playing with an intercom in the room when the voice of Christian says "Let it go, Jack." This is a phrase that he has been known to say to Jack in the past. In S3E22,
Through The Looking Glass, in a flash-forward, Jack twice makes implication that his father is still alive. He presents a prescription that is supposedly written by his father, and tells Dr. Hamill that he should get his father to see which of them is more drunk. While these last two could be the result of lies or a delusional Jack, all these incidents add up to even more mystery surrounding Christian's death and location of either him, or his body.
