Beowulf "oozes" skill. His bravery, his combat skills, and his strength are evident in the way that he walks, carries himself, talks, and dresses. A good example of this occurs when Beowulf is on his way to see Hrothgar. A guard stops Beowulf in order to know Beowulf's purpose. I am sure that the guard is wary of Beowulf's abilities because he comments on the physical presence that is Beowulf.
"Nor have I seen
A mightier man-at-arms on this earth
Than the one standing here: unless I am mistaken,
He is truly noble. This is no mere
Hanger-on in a hero’s armour."
I can give a few specific examples of Beowulf's strength. The first is the fact that Beowulf rips off Grendel's arm. He does not cut it off. He rips it off with his bare hands.
The monster's whole
body was in pain, a tremendous wound
appeared on his shoulder. Sinews split
and the bone-lappings burst. Beowulf was granted
the glory of winning; Grendel was driven
under the fen-banks, fatally hurt,
to his desolate lair.
Before Grendel's arm is brutally removed from his body, Grendel knows that he is in trouble. Remember that Grendel is said to be demon possessed in some way, and nobody has been able to beat him in combat. Grendel is likely confident that the outcome will be the same against Beowulf. Then Beowulf begins wrestling and grappling with Grendel, and Grendel realizes that Beowulf has skill and strength beyond any man that he has faced before.
The captain of evil discovered himself
in a handgrip harder than anything
he had ever encountered in any man
on the face of the earth. Every bone in his body
quailed and recoiled, but he could not escape.
He was desperate to flee to his den and hide
with the devil's litter, for in all his days
he had never been clamped or cornered like this.
The other example that I like about Beowulf's strength is the fact that he supposedly has the strength of 30 men.
"Who valuable gift-gems of the Geatmen carried
As peace-offering thither, that he thirty men’s grapple
Has in his hand, the hero-in-battle."
There are plenty of examples of Beowulf’s strength. Beowulf himself brags about his strength when he first comes to Heorot: for one thing, he tells the story of his swimming contest with his friend Brecca, in which he swam across the ocean while wearing mail and carrying a sword for five nights, all the while defending himself from sea beasts that would drag him to the bottom. Of course, the truth of his strength is proved by his encounter with Grendel in the hall; Beowulf is able to defeat Grendel purely through the strength of his grip (“harder than anything / he had ever encountered in any man / on the face of the earth” ll 750-2, Heaney tr.), literally tearing the monster limb from limb. His tremendous stamina is proved once again in his fight with Grendel’s mother, another underwater duel in which Beowulf is only able to be victorious by wielding a giant sword, originally made for giants.