Ulrich competed at the 2006 and 2010Winter Olympics for Switzerland. In 2006, he advanced to the aerials final, finishing in 10th. In 2010, he placed 18th in the qualifying round of the aerials event, failing to advance to the final.
Ulrich made his World Cup debut in January 2003. As of March 2013, he has finished on the podium five times, with the best silver medals, in 2010/11 and 2011/12. His best World Cup overall finish in aerials is 3rd, in 2010/11.