Matholwch enters the tale as a royal suitor rather than an invader. His fleet appears off Harlech, and he asks for Branwen's hand so that Ireland and Britain may be joined in a stronger alliance. Bran, also called Bendigeidfran, consults his company and agrees. The wedding is celebrated at Aberffraw under tents, because the giant king cannot be accommodated in an ordinary house. Matholwch and Branwen marry, and the gathering initially presents their union as a connection between two powerful households.

Efnysien, also commonly spelled Efnisien, discovers that his half-sister has been married without his consent. He attacks Matholwch's horses and leaves them unusable. The Irish king prepares to depart, bewildered that a marriage honour should be followed by such an insult. Bran sends envoys and offers a replacement for every injured horse, a silver staff and a gold plate. The Cauldron of Rebirth is then added to the reconciliation. Matholwch accepts the settlement and returns to Ireland with Branwen. The vessel restores dead men the following day, but those restored cannot speak.

At first Branwen is honoured in Ireland and becomes known for her generosity. She gives birth to Gwern, who is placed in fosterage. Later Matholwch's foster-brothers and nobles revive their resentment over the horses and press for retaliation. Branwen is driven into the kitchens and struck daily by the butcher, although she did not commit the original offence. Matholwch also restricts travel so that the news cannot reach Britain. Branwen's mistreatment, and the effort to hide it from her family, become the immediate cause of the appeal that brings Bran to Ireland.

Branwen trains a starling and sends her brother a message. When Bran approaches Ireland with his host, Matholwch's advisers recommend retreat beyond the River Linon and destruction of its bridge. The river's supernatural obstacle cannot stop Bran, who makes his own body a bridge for his men. Matholwch offers to hand the kingdom to Gwern, and further negotiations produce a hall large enough to receive the giant. Branwen advises acceptance of the peace. Behind that welcome, however, the Irish conceal armed men in leather bags hung around the pillars. Efnysien discovers and kills them before the feast.

The kingship is conferred on Gwern, but Efnysien kills the child in the hall's fire and fighting breaks out. The Irish use the cauldron until Efnysien destroys it from within at the cost of his own life. Only seven of Bran's warriors survive, and the tale's account of Ireland's devastation leaves five pregnant women to begin its repopulation. These are mythic explanations of catastrophe and renewal, not a historical census. Matholwch's individual death is not narrated. His final prominence is the unsuccessful peace settlement, after which the destruction of the two families overtakes him.