Velencoso started his modelling career after he finished high school, signing a contract with Group Model Management, a Spanish modelling agency. But the beginning of his career was filled with rejection. When Velencoso went to Milan, almost every agent found him unusable. His fortunes changed when Natalie Kates, an agent from New York City-based Q Model Management opened the door for him in 2001, despite his inability to speak English. Kates started him off fresh with four new polaroids in his book and sent him to meet people. One of them was photographer Matt Albiani, who loved Andres for an editorial that he was working on. The next day Andres found himself on the set of a shoot in East Hampton, New York. After just a few days in the city, he caught the eyes of some of the industry's most famous photographers, including Michael Thompson and Francois Nars. In 2002 he booked the Banana Republic spring ad campaign and a year later starred in the Louis Vuitton ad campaign, alongside Jennifer Lopez. He signed a fragrance contract with Chanel Allure Homme Sport and became the face of Loewe in 2004. Landed his first magazine cover for Arena Homme + for the winter 2005 edition and appeared in the Jean Paul Gaultier ad campaign, with Gisele Bündchen and Diana Dondoe.
