As the curtain opens, the nuns of Nonnberg Abbey, in Salzburg, Austria, are singing their daily prayers. Formal and properly reverent, the mood is respectful until one of them whispers, "Have you seen Maria?"

Maria is a young postulant. She was raised in the magnificent mountains surrounding the city, and has trouble concentrating on her duties. She loves to spend time in the hills of her childhood, singing the songs that make her happy ("The Sound Of Music"). 

Before long, Maria learns that the children have driven off a number of governesses before her. A remark from the housekeeper gives her the reason for their misbehavior; each time they need a new governess, their father is forced to return home from his numerous trips. Aloof and strict as he is, his children love him and miss the father they remember from before their mother died.
 

Maria, however, is different from the others, and the children realize right away that this woman won't be scared off so easily. Maria does check her bed for frogs, but doesn't let the children know that she is as nervous as they are.

Her compassion, bubbly personality and ability to relate to them quickly win their respect and admiration. She introduces them to music ("Doe. a Deer...") and they quickly grow to love her, and she them. Their new happiness is threatened, however, when the Captain returns home with his new lady friend to learn that his children have been cavorting about Salzburg dressed in play clothes fashioned from the old curtains from Maria's room. He is furious, and orders her back to the Abbey. Now angry herself at his neglect, Maria begins to tell him off, citing each of the children's need for him and his attentions. The Captain is angry that she would speak to him of his own children, but is halted abruptly by the sound of the children singing sweetly in the distance. He is emotionally overwhelmed by the sound of their music, which he has banned in the house since the death of his wife. He joins them in the song, and they rush into his arms. He apologizes to Maria, and asks that she remain as governess. The children's new interest in music is not lost on a family friend. Max Detweiler, a government official, frequent visitor and somewhat of an uncle to the children, wants them to sing as contestants in the Kaltzberg Festival. For the good of Austria, he says, but the Captain is adamant that his children will never sing in public.

While dancing together, both Maria and Georg sense that something is happening between them. Maria is rattled and quickly leaves his arms, claiming that she does not remember any more steps. This scene is also witnessed by Baroness Schraeder. The highlight of the evening is a performance by the children of a song bidding the guests goodbye ("So Long, Farewell"). Georg is reluctant to allow them to sing at all since he still considers it inappropriate for his children to sing in public, but Elsa Schraeder convinces him to allow it.  The guests are thoroughly charmed. After the party, we see Maria, her bag and guitar in hand, leave the house without a word.

The children are upset by Maria's sudden and unexplained departure. The Captain questions what they did to her. Nothing, they say. He is as perplexed as they are. Elsa tries to make friends with the children, but they are unhappy. The news that their father will marry her is greeted with little enthusiasm.

During their honeymoon, the Anschluss occurs and the Nazis occupy Austria. Max has entered the children in the Kaltzberg Festival without their father's permission, planning to secure it at the last minute. Upon their arrival home,  Captain von Trapp receives orders to report immediately to Bremerhaven to enter the German Navy. To buy time to plan an escape, he argues that the children, Maria and he are to sing in the festival. Max backs this statement up by producing a copy of the festival program. George is also surprised to see the program, but covers his ignorance well. It is agreed that the Captain will be escorted directly from the festival to accept his new commission, but the family manages to flee after their last number. They are hidden by the nuns in the Abbey until the Nazi searchers are gone. The  Captain claims that the mountains had always been his friends, now they had become his enemies. Mother Abbess assures him that they remain his friends; "I will lift up mine eyes unto the hills from whence cometh my help." With a new conviction that they are doing the right thing, the family begins their long hike up into the mountains, and freedom.