Beowulf is a traditional, stereotypical heroic man. In history and literature, there is an archetype of the masculine hero, and this is the type we observe in his story. The traits that it illuminates for the Anglo-Saxon idea of masculinity is primarily physical strength and the ability to conquer. Like Hercules or Oedipus, he is a very strong man who can take down mighty beasts and engage in impressive feats of strength. He is also a leader of his people and can conquer his enemy.
Violence is a common thread in the stereotype of masculinity, which is why young Spartan boys were sent to military school from the time they were five years old. Beowulf is not only physically strong, he shows his strength through his violent conflicts with Grendel and the dragon.
To an extent, these traits are still lauded. With strength competitions and a heavy emphasis on physical fitness for men in the media and entertainment industries, it is clear that strength is still important. The archetype may not be explicitly encouraged, and there is a tendency to discourage violence, but the same traits are encouraged and found desirable.
The character of Beowulf is typical of heroic epic. He is, in many ways, the ideal hero, evolving from a modest young warrior with great potential to one who does great deeds and finally to a wise and powerful king. His first and most obvious characteristic is martial prowess which he demonstrates by engaging in athletic contests as a youth (the swimming challenge) and then by killing monsters as an adult. As well as being strong and skilled in the arts of war, he is also of good moral character, acknowledging and fulfilling debts and obligations, and willing to risk or even sacrifice his own life when needed for the greater good (e.g. the fight against the dragon). He exists within a strongly hierarchical society and one that respects the bonds of kinship and hospitality, and he demonstrates the important value of loyalty.
This tradition of admiration of physical prowess, tribalism, and hierarchy is still present in the military and in team sports although technological advances do mean that the skilled engineer is now more valuable to the military than someone who can just lift heavy weights or shoot a bow accurately. Similarly, the loyalty to a small group defined by kinship and hospitality exchange is one that is admirable in some ways but in other ways can lead to narrow-mindedness and hostility to outsiders, not traits that are admirable or productive in a globalized and multicultural world.