The Lambchops are your average family, living in an average town: Dad – an awesome interpreter of bedtime classics; Mom – as smart as she is pretty; Arthur – the little brother; and Stanley – just your average kid, doing regular things ("Meet the Lambchops").

Mr. and Mrs. Lambchop tuck the boys into bed. They tell them that, if you wish upon a falling star, your wish might come true ("Lambchop Lullaby"). Arthur questions the science behind the idea, but Mr. and Mrs. Lambchop just tell the boys to go to bed.

Once the lights are out, Stanley asks Arthur what he would wish for on a falling star – an A on his science test. Stanley, however, has bigger and better ideas. He would wish to be a wizard like Harry Potter or a Jedi like Luke Skywalker, so he could have real adventures ("I Wish You Were"). The boys then see a falling star, and Stanley makes his wish to travel the world, but nothing happens. Arthur suggests that it works like Santa or the Tooth Fairy and that Stanley should go to sleep.

That night, Stanley has what he thinks is a dream. His bulletin board comes to life and informs Stanley that it can grant his wish. Stanley is skeptical and quickly falls back asleep ("Stanley's Wish"). The next morning, the Lambchop family wakes to find the bulletin board has fallen on Stanley. They become more alarmed when they move the board to find that Stanley has become flat ("Flatcakes for Breakfast"). Mrs. Lambchop is beside herself and has no idea what to do. She feels hopeless ("My Child Is Flat").

Eventually, Mr. and Mrs. Lambchop decide that Stanley needs to see Doctor Dan. While Arthur goes to school, Mrs. Lambchop takes Stanley to the doctor. On the way out the door, they run into Mrs. Cartero, who can tell there is something different about Stanley, but cannot figure it out. At the doctor's office, an utterly confusing conversation ensues, but Doctor Dan is able to offer a diagnosis: Stanley is flat. There is unfortunately no cure. Exasperated, Mrs. Lambchop takes Stanley home.

Back home, Mr. Lambchop confirms that, despite his flatness, Stanley feels fine. He gives Stanley a letter from Samantha, Stanley's best friend who moved to California. Stanley wishes he could go visit her, but plane tickets are too expensive. Mr. Lambchop thinks Stanley needs to go back to school, but Stanley is worried the other kids will laugh at him. His parents tell him not to worry and convince him to keep a positive attitude throughout every situation ("The Funny Sunny Side").

When Stanley returns to school, his plight becomes the talk of the students; the cool kids decide to use Stanley as a kite, but he gets stuck in a tree. Rather than helping him, Arthur runs to catch the bus. Up in the tree, Stanley wallows in his misfortune. As he reflects, Stanley decides that he should take advantage of his situation and go on an adventure ("In a Tree"). Mrs. Cartero finds Stanley in the tree, and he explains that, since he is so flat, his father has suggested he send himself in the mail. Mrs. Cartero agrees with the idea! With his flatness, she can just stick a stamp on Stanley, and he can go anywhere he wants to through the mail. With the help of Cartero, Stanley says goodbye to his family and gets ready to visit Samantha in Los Angeles ("Travelin' through the Mail").

In L.A., Stanley meets a powerful Hollywood Agent. The slick Agent sees something in Stanley ("Talent") and informs him that, if he travels the world and does something amazing, Stanley will finally find his own true talent. The Agent gives Stanley a cell phone and suggests he stop by the Louvre Museum in Paris. But, just then, Stanley runs into Samantha. Once the two have caught up, she encourages him to go to Paris and visit the Mona Lisa. He agrees and embarks on his journey. While en route, Arthur writes Stanley a personal letter. His family is worried about him; Arthur and Mr. and Mrs. Lambchop want to make sure everything is okay. Arthur also apologizes for the tree incident ("Arthur's Letter").

Later, in Paris, museum curator, O. Jay D'Art, expresses concern over a sneak thief who has been stealing the paintings; two of those paintings (Napoleon and Mona Lisa) are also very worried that they are at risk of being stolen from their home. To help, Stanley agrees to secretly pose as a painting in the hopes of identifying the thief. The plan works, and Stanley saves the day. Stanley then gets another letter from his Mom and Dad. He realizes that he misses his parents terribly ("Mom and Dad's Letter"). Suddenly, his cell phone rings: the Hollywood Agent has heard of his success with the thief and is offering him a part in a surfing movie in Hawaii, where Stanley will play the surfboard! Excited, Stanley heads to Honolulu ("Surfin' the Mail").

After the surfing movie makes Stanley a star, the Hollywood Agent hands him a stack of offers, but Stanley is having second thoughts: he is ready to go home. The Agent is incredulous, but Stanley is insistent, so the Agent puts him in an envelope and sends him home.

Mrs. Cartero happily delivers Stanley to his family, and they are all very surprised to see him. Stanley admits how much he has missed them, and they all hug each other tightly. When they release the hug, Stanley is no longer flat! Mr. Lambchop asks Stanley if he is okay with being back to his old self, and Stanley replies that he can have adventures every day at home, just by sending letters. This isn't the end of the adventure, but only the beginning ("Travelin' through the Mail – Finale").