Sunder (Raj Kapoor), Gopal (Rajendra Kumar) and Radha (Vyjayantimala) are three childhood friends.

Although Gopal and Radha have always loved each other, Sunder is oblivious to this and always compels his friend Gopal to ask Radha's parents to let Sunder marry Radha. Radha's parents reject Sunder's proposal on the grounds that he is a drifter and is not capable of supporting their daughter after marriage.

Though heartbroken, Sunder decides to go away to join the armed forces and become worthy of asking Radha's hand in marriage. Sunder leaves his friend Gopal to take care of his beloved Radha. Upon hearing that Sunder is missing in action and feared to be dead, Gopal and Radha are given the blessings of her parents and they wait for the day they would marry.

It is now that Sunder re-appears on the scene. Gopal is faced with the dilemma of not hurting his friend by telling Sunder the truth, Radha will not sacrifice her love and happiness for his sincerity towards his friend.

How these friends, who are separated by the twist of fate, meet - is what Sangam is all about.