Elias was picked by New Jersey 51st overall in the second round of the 1994 NHL Entry Draft but decided to stay in the Czech Republic with Kladno for one more year before going to the NHL. At only 19 years of age, Elias refused the chance to play junior hockey with the OHL's Sarnia Sting, who had picked him third overall in the 1994 Import Draft. Instead, he immediately joined a powerful Devils team that would win the Stanley Cup in 1995.
In 1995-96 Elias appeared in just one New Jersey game and spent most of the season playing for the Albany River Rats in the AHL. He bounced around between the River Rats and the Devils for the next two seasons, making the 1996-97 AHL All-Star game and registering 51 goals and 79 assists for 130 points in 131 total games in Albany in the process.
Impressed by his stats and his hard work in the AHL, management moved Elias up to the NHL for the 1997 playoffs and he produced immediately, scoring five points in eight post-season games. The following season, New Jersey called him up to the NHL again and he immediately met the challenge of big-league play, scoring 18 goals and registering 19 assists that year and finishing third in the balloting for the Calder Trophy as the NHL's best rookie. Close observers of the game noted that only Calder winner Sergei Samsonov of Boston scored more goals than Elias, and only Samsonov and Toronto's Mike Johnson had more points.
The one significant downside to Elias's career in the NHL since making the move to the big time came in 1998 when he failed to make the powerful Czech Olympic team that ended up winning top honours at the Winter Games in Nagano, Japan. However, Elias would get his opportunoty to shine with his homeland at the 2002 Winter Olympic Games in Salt Lake City, Utah.
In 1999-00 Elias went on to score 35 goals and 72 points in the regular season, and was instrumental in leading the Devils to their second Stanley Cup victory.
Elias established career highs in goals (40), assists (56) and points (96) in 2000-01 leading the Devils to the Stanley Cup Final for a second consecutive season before falling short against the Colorado Avalanche.
A member of the Czech Republic's Olympic Team in 2002 and One of the premier players in the league, Elias captured went on to capture his second Stanley Cup title in 2003 despite having his least productive season offensively since the 1998-99 tallying 57 points (28-29-57). Elias rebounded offensively in 2003-04 with 81 points (38-43-81), yet the Devils fell short in their attempt to repeat as Cup champions.
While playing hockey in Russia during the NHL lockout, Elias' health took an unexpected turn for the worse when the Czech forward contracted Hepatitis A. His bout with Hepatitis weakened him and as a result Elias lost 30 pounds and didn't return to the NHL until January, 2006.
On the international stage, Elias has represented his native Czech Republic ten times. This includes four Winter Olympics (2002, 2006, 2010, 2014) and won a Bronze Medal in 2006. He also has appeared in four IIHF World Championships (1998, 2008, 2009, 2011) and one World Cup of Hockey in 2004.