Elwood made his debut for Connacht against Scottish North & Midland, at inside centre, on 18 September 1989. He scored the first of his 8 tries for Connacht a month later, 21 October 1989, against Munster in the Sportsground when tries were still only worth 4 points. He was the first Connacht player to score over 1,000 points for the province. By the time he made his final appearance, against Sale on the 24th of April 2005, Elwood had scored 8 tries, 141 conversions, 7 drop goals and 268 penalties, a total of 1,152 points. His number of appearances for Connacht was also the record until November 2009, when
Michael Swift overtook him. When Elwood was first capped for
Ireland, he was playing for
Lansdowne, but he later returned to
Galwegians, the club of his youth. 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. Eric also participated in the inaugural
1993 Rugby World Cup Sevens held in Murrayfield, where the
Ireland Squad reached the semi-final, losing out to eventail runners up Australia. In 1993, Elwood was called up for the
Barbarians invitational side. He played against at
Cardiff Arms Park. The Barbarians lost the game 12–25, with Elwood scoring all of the team's points, converting four penalties. Elwood also played
Gaelic Football for
Galway appearing in the 1990 Connacht Football Final defeat to Roscommon. ==Coaching career==