Sudová made his debut on January 9, 1999 in the Freestyle Skiing World Cup and reached 31st place in Mont Tremblant . Due to injury, she had to skip the entire 1999/2000 season. She got World Cup points for the first time on December 14th, 2000 as 26th in Tignes . Due to insufficient performance, she was transferred to the European Cup in the second half of the season, where she was able to win five times in a row. At the beginning of the 2001/02 season, she came in Tignes for the first time in the top ten of a World Cup race.
In the winter of 2002/03 Sudová established himself in midfield, at the 2003 World Cup in Deer Valley , she achieved two top 10 results. In the 2003/04 season she slowly began to approach the world elite, with fourth place as her best result so far. On January 8, 2005 Sudová was able to win their first World Cup race in Mont Tremblant, which was followed by four more podium places. At the end of the season, she won the silver medal in the Moguls competition at the 2005 World Cup in Ruka .
After Sudová had achieved two more podium places in the 2005/06 season, she won a World Cup race for the second time on March 18, 2006 in Apex . At the 2006 Winter Olympics , she was sixth. In the 2006/07 season it was enough for her to finish fourth three times and at the 2007 World Cup in Madonna di Campiglio to two further top 10 placements. In the winter of 2007/08, Sudová stood on the podium four times in the World Cup and was never worse than seventh, in the discipline she only had to admit defeat to the series winner Aiko Uemura .
Another four times on the podium was Sudová in the 2008/09 season, each time only a little was missing to another victory. At the 2009 World Championships in Inawashiro , she won the Mughal bronze medal. Another two podium places were added in the current 2009/10 World Cup season.