The apple tree is a symbol of Larry. The tree was planted to commemorate him. The tree's death symbolizes the way the older Kellers will finally come to fully accept Larry's death.

A high wind causes the apple tree to snap and fall over the night before the action of the play starts, leaving nothing but the stump. Throughout the play, characters comment on the fallen tree. For example, Frank, who is doing Larry's horoscope, comments that it is interesting that the tree was killed so close to Larry's birthday, August 25.

Mrs. Keller, however, seems to be the one who connects the apple tree most fully with Larry. Her words inadvertently show how the tree's fate foreshadows the way everything in the play will happen all at once, as well as the way the past will come back to haunt them all:

It's so funny ... everything decides to happen at the same time. This month is his birthday, his tree blows down, Annie comes. Everything that happened seems to be coming back.

Later, she connects the falling of the tree to Larry's suicide, again without realizing what she is doing:

The wind ... it was like the roaring of his engine. I came out here ... I must've still been half asleep. I could hear that roaring like he was going by. The tree snapped right in front of me ... and I like ... came awake.

Apple trees have a deep connection in Western thought with the fall of Adam and Eve from paradise. When Adam and Eve eat the fruit of the forbidden tree containing the knowledge of good and evil, their lives are forever changed. When Mr. and Mrs. Keller finally accept Larry's death and their complicity in it, they fall into a new knowledge of good and evil that is equally life-changing for them.

What is the significance of the apple tree and the letter in relation to the action of "All My Sons"?

The apple tree is symbolic in many ways. First, it was planted in the memory of Larry, the eldest the the Keller children whose plane was shot down in the World War II. Apple trees are universal symbols for the sin and the fall of mankind from the garden of Eden. Trees are also personified as men in the Bible. In Song of Songs, the apple tree is also associated with mothers and sons and also, sons and lovers.

In Song of Sons 8:5 we read:
"Who is this that cometh up from the wilderness, Leaning upon her beloved? Under the apple-tree I awakened thee: There thy mother was in travail with thee, There was she in travail that brought thee forth."

In Son of Songs 2:3, As the apple-tree among the trees of the wood, So is my beloved among the sons. I sat down under his shadow with great delight, And his fruit was sweet to my taste. (ASV BBE DBY JPS WBS)
The the apple tree foreshadows some kind of break in the relationship between Larry's mother, who still believes he is alive, and also the blossoming relationship between Chris and Ann. The tree can also be seen as representing the Keller household which hides the sin of the father That sin and its consequences are about to break the family apart. The significance of the letter is that it proves that Larry was suicidal over his father's crime and that he was planning to let himself be shot down. The letter shows that Larry was like the apple tree, torn apart by the story over his father's actions.