Give details that support the claim that Beowulf is a round character.
I guess I'm looking for details that would make a reader think that he is a round character, even though he is pretty much a flat character.
I must agree with you when adhering to the definitions provided that Beowulf is a flat character.
A flat character is a minor character in a work of fiction who does not undergo substantial change or growth in the course of a story.
A round character is a complex literary character with fully developed and dynamic traits.
Beowulf is a known hero. The only reason that Hrothgar accepts Beowulf's help is because he knows of him through the epic tales told regarding the heroic tales Beowulf has partaken in.
But, sometimes it makes a text more interesting to try to prove something different.
Therefore, to support that Beowulf is a round character, one must look at how he is developed for the "new" reader.
In the opening of Episode One, Beowulf is first described:
Now Beowulf bode in the burg of the Scyldings,
leader beloved, and long he ruled
in fame with all folk
Here readers learn from where Beowulf comes and that he is a loved ruler (both provide the development of who Beowulf is).
In the conversation between Beowulf and Unferth, readers find out that many people, outside of Beowulf's kingdom, know of the heroism of Beowulf. This, again, attributes to the "roundness" of Beowulf's character- readers are learning more about him as a warrior and hero.
Later, readers learn about Beowulf's internal strength and morality. He chooses to fight the monster Grendel without weapons- so that the fight be fair:
Not with the sword, then, to sleep of death
his life will I give, though it lie in my power.
No skill is his to strike against me,
my shield to hew though he hardy be,
bold in battle; we both, this night,
shall spurn the sword, if he seek me here,
unweaponed, for war.
Although those who speak of Beowulf know him well and he does not seem to change as a man (is and remains a hero), readers learn about Beowulf's notoriety through the text itself. Therefore, one could justify that Beowulf is a round character based solely upon the fact that his history, his battles, and his abilities are immaculately detailed.
This question has already been asked and answered many times here on eNotes. Here is a comprehensive link for you: http://www.enotes.com/search?q=beowulf+round+character
Yes, but this is by far the best answer that I have come across.