Mud
Mud is the title of the play. Mud is a physical reality of the set design. Mud is referenced as the place where pigs live, and things are left to rot and die. Mud is a symbolic conglomeration of many things: poverty, hopelessness, death and more.
Ironing Board
In several of the scenes, Mae is showing ironing clothes or closing the ironing board and settling it back against the wall. The ironing board has a long, rich history as one of the iconic symbols of patriarchal oppression of women.
The Textbook
The textbook from which Mae several times reads about different sea animals holds a place in her limited universe that is held in millions of others by the Bible. The textbook is where she goes in her continuing efforts to find a sense of purpose and place in the world; the passages chosen are her attempt to understand herself.
Lipstick
Henry’s gift of lipstick for Mae is a different sort of symbol of the patriarchal oppression of women. If the ironing board represents how men subjugate women into the submissive role of caretaker, the lipstick symbolizes how the ultimate misogyny in that subjugation: do the dirty work, but look pretty for me while doing it.
The Rifle
These characters don’t have much. Mae’s one prized possession is a textbook. And when Mae is given the gift of lipstick, it is as though she has never even heard of it before. And yet, unsurprisingly, they do a rifle. Because, of course they do, being American and all. The rifle here symbolizes what guns always symbolize ultimately: the ability to exert control over another’s actions, over another’s dreams, over another’s decision to say “no!”