Conflict in literature typically refers to a struggle experienced by the main character. In “The Invalid’s Story” by Mark Twain, the surface-level conflict is man vs. self. The narrator in Twain’s tale is struggling with his feelings regarding the death of his friend. He describes his mood as the train leaves the station by stating the following: “a cheerless misery stole over me, my heart went down, down, down.” When he begins to detect the horrible smell, he is depressed and saddened by the thought of his friend’s corpse. Twain further demonstrates the protagonist’s sadness with the line, “there was something infinitely saddening about his calling himself to my remembrance in this dumb pathetic way.” As the narrator makes each attempt to lessen the horrible stench, he is again reminded of his friend’s demise and his own sadness.

“The Invalid’s Story,” on a deeper level, is really about man vs. fate. The narrator realizes that death is inevitable. Although the bulk of the story centers on the narrator’s journey with his friend’s corpse, or at least what he believes to be his corpse, the reality is the corpse is just a reminder that everyone must die. Thompson even goes into a rant about how “we all got to go” when discussing the corpse. Twain ends the story with the narrator stating “he is on his way home to die.”

There are many conflicts, and many types of conflict, in this story (if you define "conflict" as any sort of clash or disagreement). The first is between the stories told—how old is the narrator?
The second is a restatement of what the box being transported contains.
The third is a conflict between the smell and comfort, and the fourth is confusion over the source of that smell (cheese or dead body).

Cigar smoke vs. cheese smell.

All these stresses vs. the narrator's health.

And subject matter (serious) vs. tone (humorous).