Sangam, the first colour film produced and directed by Raj Kapoor and the first film for which the showman shot abroad, is a classic love triangle with two friends in love with the same woman. Sundar (Kapoor), Gopal (Rajendra Kumar) and Radha (Vyjayanthimala) are childhood friends. As they grow up, the extrovert Sundar is attracted to Radha, but she prefers the more subdued Gopal, who also loves her but sacrifices his feelings for his friend's sake.
Sundar joins the air force and is sent on a mission in Kashmir. Before leaving, he makes Gopal promise to look after Radha and not let anyone come between himself and her while he is away. But his plane is shot down over Kashmir and he is presumed dead. Radha and Gopal, though grief-stricken, are now free to express their love for each other. Gopal sends her an unsigned love letter which she keeps safely.
However, before they can marry, Sundar returns, alive and well, celebrated as a war hero, and declares that it was only Radha's love that helped him live. The self-effacing Gopal withdraws again and Radha, feeling duty-bound, marries Sundar. She also tells Gopal, whose very presence now troubles her, to stay away from the couple. Sundar, however, keeps trying to draw his buddy into their life.
Then one day Sundar discovers the love letter and all hell breaks loose as he thinks Radha has cheated on him. He demands that she name the lover and threatens to kill him. Radha refuses to reveal anything and Sundar becomes obsessed with discovering the letter writer, making her very life miserable. Finally, she leaves her marital home and goes to Gopal for help. Sundar, unaware that Radha has gone to Gopal's house, also arrives there to seek his friend's help. Matters come to a head and Gopal admits writing the letter, an admission that almost breaks Sundar. Unable to convince his friend that he and Radha did not cheat on him, Gopal grabs Sundar's pistol and kills himself.