Kass grew up in the Estonian city of Paide. When she was little girl, she lived in Sika village. Her mother worked in farm. There, she was brought up by a single mother and lived in a cramped apartment. At the age of fourteen, she was 'discovered' in a Tallinn supermarket by an Italian modeling scout. Kass had wanted to compete for the Miss Estonia title, but an offer to fly to Milan, Italy, to start a modeling career seemed like a more glamorous and lucrative option. Kass officially moved to Paris at the age of 18. Soon after, she received exposure on the cover of magazines worldwide, such as Vogue (France) in 1997, ELLE (Australia), Image (UK), Madame Figaro, Numero France, Vogue (France), and Vogue (US) in 1999.

In 1999, Kass modeled for top designers such as Marc Jacobs, Michael Kors, Calvin Klein, Ralph Lauren, Donna Karan, Dolce & Gabbana, Gucci, Prada, Versace, Fendi, Chanel, Chloe, Valentino, Louis Vuitton, and Givenchy. In addition, Kass has posed in numerous advertisements for Calvin Klein, Chanel, Donna Karan, Givenchy, Fendi, Michael Kors, Versace, and also for General Motors. She is also recognized for her appearances in a The Gap denim advertising campaign. Kass was a spokesperson for Sephora, one of the world's leading cosmetics retailers, and the Christian Dior perfume, J'adore.

Kass was awarded by Vogue as "Model of the Year" at the 2000 VH1/Vogue Fashion Awards. As of 2006, she has appeared in campaigns for Dsquared, Pedro del Hierro, Michael Kors and Chloe with Malgosia Bela. In 2007, Kass has got ten campaigns only for the spring/summer collection, including Versace, Michael Kors, Pucci, Jones New York, Salvatore Ferragamo, Gap, Peek & Cloppenburg, Bedat & Co, Time and Et Vous?.