What is the main problem in the story of Beowulf?
The main problem in the story of Beowulf is actually a little more difficult to pinpoint than you might think, because the poem actually incorporates three major conflicts. The first (and most famous) problem is the conflict between the monster Grendel and Hrothgar, the king of the Danes. It is this conflict that first brings Beowulf to Heorot to perform his deeds of heroism. After Beowulf defeats Grendel, however, he must then also fight and subdue Grendel's mother, who attacks Heorot to avenge her son's death. Following this conflict, Beowulf returns to his homeland, eventually becomes king, and then rules for many years before fighting an attacking dragon and dying in battle. As such, you can see that the poem revolves around three major problems (or conflicts), rather than one. However, if you had to pick one, single problem, then you could argue that the main problem of the story is the conflict between Beowulf and the Grendel family (which includes both Grendel and his mother), as this feud takes up the bulk of the poem once its two components are grouped together.
The main conflict in Beowulf is that of the human hero versus the monster. Although some degree of intelligence is required of the hero in planning tactics, the conflict is overwhelmingly physical; the hero overpowers the monster by means of strength and martial prowess.
There are three major fights of this type in the poem. First, the monster Grendel has been attacking King Hrothgar's mead hall, Heorot, and killing the Danish warriors inhabiting it. Beowulf and his men come to the defense of the Danes and eventually Beowulf triumphs over Grendel in single combat.
Next, Grendel's mother takes revenge for the death of her son by attacking Beowulf and the Danes. Beowulf tracks her back to her undersea lair and eventually decapitates her with his sword.
The final conflict involves Beowulf defending his people from a dragon. In the battle, Beowulf succeeds in killing the dragon but dies from his wounds.