He is a composer and arranger of experimental Venezuelan music, member of the group of the renowned flutist Huáscar Barradas, with an exquisite musical taste that has led him to be considered one of the most prominent musicians in the region. He has also shared the stage with great artists such as Ílan Chester, Lilia Vera, María Teresa Chacín, Aldemaro Romero, Gustavo Colina, Gualberto Ibarreto, Frank Quintero, Alexis Cárdenas, among others.

With the musical group of Huáscar Barradas he has recorded fifteen musical productions, participating as bassist, guitarist, arranger and musical co-producer. He has toured with this group nationally and internationally representing Venezuela at the Expo 2000 in Hanover, Germany and in the United States, at the Flute Festival in Columbus, Ohio, and the International Flute Festival in Quito, Ecuador. They also performed in London at the Bolivar Hall.

In October 2003 he toured with Cecilia Todd, Huáscar Barradas and Jorge Polanco in countries such as Japan, the Philippines and South Korea, in a cultural event called Cultural Week of Venezuela in Japan, Philippines and South Korea. In 2004 he toured several cities in Spain performing at Calle 54, a jazz club considered one of the most important in Europe.

Elvis Martinez has also made important concert tours with Maestro Alexis Cardenas and his group Alexis Cárdenas Cuarteto through several countries in Europe and Latin America, performing in several music festivals such as the Sull Acqua Music Festival in Italy in 2010 and 2011, also in the Classique au vert Festival in Paris in 2012, in the Medellin International Festival and the Cartagena International Festival, both in Colombia in 2013 and also participating in concerts in Ecuador. He travelled to Kuala Lumpur in Malaysia, performing at the Petronas Towers. He also participated in the Brussels International Festival in Belgium. He has recorded three musical productions with Alexis Cárdenas Cuarteto. Elvis Martinez also made an important tour with the great cuatro player Miguel Siso in Beijing, China in 2013, making several concerts in the Beijing History Theater.

In March and April of 2016, he made a tour with Huáscar Barradas called Trio Acústico Venezolano, in several cities of the United States like Phoenix, Miami and Houston. Also, in 2016 he toured some cities in Turkey and Belgium. Elvis Martinez was also an active member of the Maracaibo Symphony Orchestra for 26 years and professor of the double bass cathedra at the Jose Luis Paz Music Conservatory for 17 years until 2017, where he trained the new Venezuelan talents that today stand out on stages around the world.

In 2018, he participated in the production of Miguel Siso's album Identidad as a double bass player, which won the Latin Grammy in the category Instrumental Music. In addition, in 2019, he participated as a double bass player in the homonymous tour of this album in the United States, which consisted of 4 concerts in the cities of Miami, Orlando, New York and Houston, organized and sponsored by Guataca Producciones.

Elvis participated in 2019, in 20 concerts of the very successful musical theater play written by Cesar Miguel Rondón called En la vida hay amores, with the singers Lena Burke and Rafael "Pollo" Brito, accompanied by four musicians, among whom Elvis Martinez was the double bass player in 12 concerts and the guitarist in 8 concerts, with full halls at the Colony Theater in the city of Miami. Elvis Martinez had also in 2019 participation in concerts of the Jazz genre in various Jazz clubs in the city of Miami, highlighting his participation in the important Four Seasons Hotel with bassist Rodner Padilla, winner of three Latin Grammys.

In December 2019, he participated with Huáscar Barradas in a small Christmas concert tour for children called Hallacas con Flauta, which visited cities such as Houston, Indianapolis, Miami and Orlando, where musical genres as the Gaita Zuliana, the Parranda Zuliana and the aguinaldos among other typical Venezuelan Christmas genres stood out.