There are multiple internal and external conflicts within "A Streetcar Named Desire". For purpose of ease, I will go through the characters and the conflicts that they face.
Blanche DuBois: Blanche faces one main internal conflict and many external conflicts. Blanche's main internal conflict is her lack of youth. She constantly struggles with the fact that she is no longer a young woman. She feels as though she is at the end of her attraction to others. Another internal conflict which Blanche faces is the loss of her true love. The recurring thoughts of his death torment her. Eventually, Blanche loses the battle with her sanity and is committed to a mental asylum.
As for the external conflicts, Blanche faces many. 1) Blanche cannot forgive Stella for leaving Belle Reve. 2) Blanche is forced to face Stanley given the loss of Belle Reve. 3) Stanley rapes Blanche. 4) Blanche cannot be happy in the home of her sister given the environment. 5) Blanche dislikes light given it shows her true "colors".
Stella Kowalski: Stella really only has one main internal conflict. She struggles with the fact that her sister does not approve of her life. In the end, her struggle is with believing if Stanley raped Blanche, a fact that she could not believe and still stay living with Stanley.
As for Stella's external conflicts, the main one exists between her and Stanley. Stanley is an abusive husband. Unfortunately, the play itself shows this as typical of the environment (other characters are seen abusing each other as well- and just going on with life).
Stanley Kowalski: Stanley's main internal conflict stems from his external conflict with Blanche. Blanche, during a conversation with Stella, called Stanley uncivilized. Stanley is a man who holds pride very high on his list- Blanche forced him to question his own manhood. Stanley holds Blanche's presence as a bother and eventually it becomes an internal conflict which needs her removal to fail to exist.
Externally, Stanley (as stated in Stella's conflict area) fights with Stella physically. Alcohol can also be seen as both an internal and external conflict attributer for Stanley. Externally, alcohol is an item that causes problems for Stanley. Internally, Stanley cannot handle drinking and inner anger erupts.
Mitch Mitchell: Readers are not given much of Mitch's point-of-view. Basically, he exists as a subordinate character that provides insight into Blanche's character. Regardless, readers are shown two specific conflicts that Mitch faces.
Internally, Mitch faces the conflict of eventually leaving his mother. His is portrayed as a "momma's boy" and the thought of leaving her causes confusion and pain for Mitch. Mitch knows that Blanche lies to him about her age, but it is not that which causes him the concern. Instead, Mitch is conflicted about Blanche's sorted past.
There are a series of internal and external conflicts within the play "The Street car Named Desire."
Blanche battles her own aging process and lack of self-identity. She finally loses her mind when confronted with the truth about herself.
Stella and Stanly conflict as man and wife. Stanley is dominating, controlling, and abusive. The two have a violent and passionate relationship which they continue to stay in after disaster unfolds with Blanche.
Mitch is lonely and wants a mate. He meets Blanche and intends to marry her. He finds out the truth about her. He decides it may be better to be single than to be married to a slut.
Stanley hates Blanche's presence in his marriage. He helps send her over the edge to insanity. He returns to his life with just Stella and him.
Blanche has no where to live, eat, and sleep. She goes crazy at Stella's and gets to live at a mental asylum for free with meals included.