Elik played three seasons in the Ontario Hockey League with the Kingston Canadians and North Bay Centennials before turning professional.

He made his pro debut with the International Hockey League's Colorado Rangers, and he scored 100 points (44 goals and 56 assists) in his first season.

The Minnesota North Stars acquired Elik before the 1991–92 season, giving up Randy Gilhen, Jim Thomson, and a fourth-round draft pick (which became Alexei Zhitnik) for him.

After playing in 18 games with the Oilers, Elik was placed on waivers and claimed by the San Jose Sharks.

After a brief stint with the St. Louis Blues and two seasons with the Boston Bruins organization, Elik left North America to play professionally in Europe.