Dead Sons

Macbeth has several dead sons in it--two out of three to be specific. 

Siward's son dies, which is interesting because we hardly know Siward and know even less about Young Siward. All we know is Macbeth kills Young Siward, probably for the purpose of just making Macbeth seem even crazier and more tyrannical than we already thought of him. Old Siward took it rather coldly when he found out--he seems happy that his son died fighting and not cowardly. He even wishes he had as many sons as he had hairs on his head so that they could all die bravely. This does not seem like a good lineage plan. When Malcolm offers sympathy for the loss, Siward wants none of it, so we can argue that Siward did not value his progeny. 

Earlier in the play, Macduff's son is killed by murderers sent by Macbeth. This ends his lineage as far as we know which explains why there are so few Macduff's in the world now. This son's death motivates Macduff to want to personally kill Macbeth which is important, because Macduff wasn't born of a woman as is the only person in Scotland that can kill Macbeth.

Shakespeare himself had a son, Hamnet, who died at the tender age of 11, about nine years before Shakespeare wrote The Scottish Play. I conjecture that these Macbeth characters dealing with their son's mortalities is a result of Shakespeare's own issues.