John Gower introduces each act with a prologue. The play opens in the court of Antiochus, king of Antioch, who has offered the hand of his beautiful daughter to any man who answers his riddle; but those who fail shall die.
I am no viper, yet I feed

On mother's flesh which did me breed.

I sought a husband, in which labour

I found that kindness in a father:

He's father, son, and husband mild;

I mother, wife, and yet his child.

How they may be, and yet in two,

As you will live, resolve it you.
Pericles, the young Prince (ruler) of Tyre in Phoenicia (Lebanon), hears the riddle, and instantly understands its meaning: Antiochus is engaged in an incestuous relationship with his daughter. If he reveals this truth, he will be killed, but if he answers incorrectly, he will also be killed. Pericles hints that he knows the answer, and asks for more time to think. Antiochus grants him forty days, and then sends an assassin after him. However, Pericles has fled the city in disgust.
Pericles returns to Tyre, where his trusted friend and counsellor Helicanus advises him to leave the city, for Antiochus surely will hunt him down. Pericles leaves Helicanus as regent and sails to Tarsus, a city beset by famine. The generous Pericles gives the governor of the city, Cleon, and his wife Dionyza, grain from his ship to save their people. The famine ends, and after being thanked profusely by Cleon and Dionyza, Pericles continues on.
A storm wrecks Pericles' ship and washes him up on the shores of Pentapolis. He is rescued by a group of poor fishermen who inform him that Simonedes, King of Pentapolis, is holding a tournament the next day and that the winner will receive the hand of his daughter Thaisa in marriage. Fortunately, one of the fishermen drags Pericles' suit of armour on shore that very moment, and the prince decides to enter the tournament. Although his equipment is rusty, Pericles wins the tournament and the hand of Thaisa (who is deeply attracted to him) in marriage. Simonedes initially expresses doubt about the union, but soon comes to like Pericles and allows them to wed.
A letter sent by the noblemen reaches Pericles in Pentapolis, who decides to return to Tyre with the pregnant Thaisa. Again, a storm arises while at sea, and Thaisa appears to die giving birth to her child, Marina. The sailors insist that Thaisa's body be set overboard in order to calm the storm. Pericles grudgingly agrees, and decides to stop at Tarsus because he fears that Marina may not survive the storm.
Luckily, Thaisa's casket washes ashore at Ephesus near the residence of Lord Cerimon, a physician who revives her. Thinking that Pericles died in the storm, Thaisa becomes a priestess in the temple of Diana.
Pericles departs to rule Tyre, leaving Marina in the care of Cleon and Dionyza.
Marina grows up more beautiful than Philoten the daughter of Cleon and Dionyza, so Dionyza plans Marina's murder. The plan is thwarted when pirates kidnap Marina and then sell her to a brothel in Mytilene. There, Marina manages to keep her virginity by convincing the men that they should seek virtue. Worried that she is ruining their market, the brothel rents her out as a tutor to respectable young ladies. She becomes famous for music and other decorous entertainments.
Meanwhile, Pericles returns to Tarsus for his daughter. The governor and his wife claim she has died; in grief, he takes to the sea.
Pericles' wanderings bring him to Mytilene where the governor Lysimachus, seeking to cheer him up, brings in Marina. They compare their sad stories and joyfully realise they are father and daughter. Next, the goddess Diana appears in a dream to Pericles, and tells him to come to the temple where he finds Thaisa. The wicked Cleon and Dionyza are killed when their people revolt against their crime. Lysimachus will marry Marina.

Question: Why can't Pericles reveal his answer? 
Answer: He fears the correct answer will get him killed.
Alternative answer: If he fails the riddle, he dies and if he solves it, he dies