Act I
At Nonnberg Abbey near Salzburg, Austria, just before World War II, the nuns are singing the Dixit Dominus. One of their postulants, however, Maria Rainer, is missing. Singing on the nearby mountainside (“The Sound of Music"), Maria is reluctant to leave her beloved hills, returning to the abbey only after the gates are locked. The concerned Mother Abbess and other nuns wonder what to do with her ("Maria"). Maria apologizes for singing in the garden without permission, and the Mother Abbess sympathizes ("My Favorite Things"), but suggests that Maria consider taking some time away, to decide whether the monastic life is really for her. The widower Captain Georg von Trapp of the Austro-Hungarian Navy has requested a governess for his seven children, and this might be a good position for Maria to take for a few months.

At his villa, von Trapp gives his butler Franz and the housekeeper Frau Schmidt instructions on how to deal with the new governess. Maria arrives and the Captain summons his children with a bosun's whistle; they march in in their Navy uniforms and are introduced: Liesl, Friedrich, Louisa, Kurt, Brigitta, Marta, and Gretl. Maria palpably disapproves of the Captain’s militaristic discipline. Left alone with the children, she learns that they have never learned how to sing! The rudiments of music, as she demonstrates, are quite easy ("Do-Re-Mi").

Rolf, the messenger boy, has a birthday telegram for Franz and encounters Liesl outside the villa. He reveals that a colonel from Berlin is visiting the local leader of the Nazi party. But he thinks Liesl should not tell her father – he knows better because he is older than she ("Sixteen Going on Seventeen"). Somehow they kiss, and Rolf runs off, embarrassed.

It is bedtime. Frau Schmidt gives Maria material to make herself some new clothes, since all her possessions were given up to the nuns for charity. Maria asks for more fabric to make play clothes for the children, but Frau Schmidt explains that they must march, not play. Maria is saying her evening prayers when Liesl, soaking wet from a thunderstorm, crawls in at the window. Maria promises to keep her secret. The other children, frightened by the storm, run in to Maria for comfort. Maria cheers them up with a song ("The Lonely Goatherd").

A month later, Captain von Trapp arrives home with two guests, Baroness Elsa Schräder and Max Detweiler. Why are the children not there to greet them? The Captain goes in search, and Elsa reveals to Max that something is preventing the Captain from marrying her. Only poor people, replies Max, have time for romance ("How Can Love Survive").

Rolf, looking for Liesl, runs into the Captain and salutes him with a "Heil!". The Captain orders him to leave the premises: we are in Austria, not Germany. Maria and her charges leapfrog into the room, wearing play-clothes made from the old curtains in Maria's bedroom. The Captain is appalled and sends them off to change and clean up. Maria tells him that his children need his love rather than discipline. He angrily orders her back to the abbey. But from the next room they hear the children singing a song Maria has taught them – "The Sound of Music" – to Baroness Schräder. The Captain is mollified – he joins in the song and embraces the children.

Alone with Maria, he thanks her for bringing music back into his house and asks her to stay. The Baroness is suspicious, but Maria reassures her that she expects to return to the abbey in September.

The Captain is throwing a party to introduce Elsa to his friends; the guests hotly discuss the Anschluss (annexation of Austria to Germany). Young Kurt asks Maria to teach him to dance the Laendler. It goes well enough for a while, but he is unable to execute a complicated step, at which point the Captain volunteers to demonstrate. Maria and the Captain eventually meet eye-to-eye, and Maria, embarrassed and flustered, breaks away.

Max arrives, and the Captain realizes that he needs another female to even out the seating at dinner; he asks Maria to take a place. Surely, objects Max, the Captain does not expect his guests to dine with a nursemaid! The Captain ignores him.

Elsa begs the Captain to let the children sing good-night to the guests ("So Long, Farewell"). Max, a producer, is overwhelmed with their talent and insists that he needs them for the Kaltzberg Festival. As the guests move toward the dining room, the dejected Maria slips out the front door with her luggage.

At the abbey, Maria tells the Mother Abbess that she is ready to take her vows as a nun. Mother Abbess, however, senses that Maria is running away from her true feelings. She advises Maria to return to the Captain’s villa and come to grips with the situation. Maria must find the life she was meant to live ("Climb Ev'ry Mountain").

Act II
At the von Trapp villa, Max teaches the children how to sing on stage, but tells the Captain nothing about it. The Captain tries to get them to sing with him, but the children complain that he doesn’t do it Maria’s way. The boys and girls try to understand why Maria is gone, and the Captain explains that he has asked Elsa to marry him. The children sing "My Favorite Things" in an effort to cheer themselves up, but fail – until they hear Maria singing on her way back to them.

Since the wedding of Elsa and the Captain is imminent, Maria decides to stay only until another governess can be found. Max and Elsa try to persuade the Captain to accept the Anschluss, as it seems inevitable ("No Way to Stop It"). The Captain is adamant, however, and Elsa decides to break off their engagement. Left alone, the Captain and Maria finally admit to loving each other ("An Ordinary Couple"). At their wedding, the nuns reprise "Maria" in counterpoint to the processional.

Soon after the wedding, Max is coaching the children for their performance at the Kaltzberg Festival. Herr Zeller, the Party Leader, arrives and demands to know why they are not flying the Nazi flag now that Austria is a part of Germany (March 12, 1938). The Captain and Maria return early from their honeymoon and the Captain refuses to allow the children to sing at the Festival. Max tries to persuade him that the children would be singing for Austria, but the Captain points out bitterly that Austria no longer exists.

Maria tells Liesl that in a few years she, too, will probably be married ("Sixteen Going on Seventeen – reprise"). Rolf enters with a telegram for the Captain, which he refuses to give to Maria, handing it to Franz instead. The telegram offers the Captain a commission in the German Navy. He decides that since he cannot accept it, the whole family must flee Austria in secret.

Admiral von Schreiber of the German Navy arrives to demand why the Captain has not answered his telegram. He learns that the Captain has just returned from his honeymoon; he congratulates him but orders him to report immediately to Bremerhaven to assume his command. Maria makes his excuse: he cannot leave immediately, as they are all singing in the Kaltzberg Festival!

At the concert, they sing an elaborate version of "Do-Re-Mi"; then Max brings out the Captain's guitar. His song "Edelweiss" (Austria's national flower) is plainly a declaration of loyalty to Austria itself. Max prevents the von Trapps from leaving the stage, asking for an encore and announcing to the audience that this is the family's last chance to sing together for a long time, for the honor guard is waiting outside to escort the Captain directly to his new command. While the judges are evaluating the contestants, the von Trapps sing "So Long, Farewell", leaving the stage in small groups. Max then announces the winners, stalling as much as possible. When he finally announces that the first prize goes to the von Trapps, they are nowhere to be found.

The Nazis send out a search party. The family hides at the Abbey, and are discovered only by Rolf, who summons a Nazi lieutenant. But after seeing Liesl, Rolf reports that he has found no one. The von Trapps, learning that the borders have been closed, are determined to flee over the mountains. The nuns reprise: "Climb Ev'ry Mountain".