Elwood played 35 times for Ireland and scored a total of 296 points. This total places him at number four in the all-time points scorers for Ireland. He also participated in two Rugby World Cups, in the 1995 tournament which took place in South Africa, and 1999's tournament, in France. He made his last appearance for Ireland coming on as a substitute in their play-off loss to Argentina at the 1999 World Cup in Lens.