Born in Monterrey, Mexico on March 24, 1891. When he turned 17, he rolled up his canvases and took a train to Mexico City with the intention of following his dream of studying at the famed Academia de San Carlos. When he got there the enrollment process had ended but as luck would have it being named Fidias, like the most famous sculptor of classical Greece, struck a cord with the dean of the school and he was given a chance to study there. Some of his fellow students went on to become well known artists like Ignacio Asúnsulo, Fermín Revueltas, Jean Charlot and Ernesto García Cabral. Alfredo Ramos Martinez, then his professor at the academy, convinced him to visit Paris, so in 1913 Elizondo boarded the famous Ipiranga and set sail to set foot in Europe for the first time. When he got to France, the first World War had started and so he had little time to study and spent most of his days working at factories building and repairing grenade launchers, cars and planes. Nevertheless it was here where he produced his first wood sculptures which would be among his most important works. He also lived in Barcelona and Argentina before returning to Mexico in 1921. Upon his return he became a professor in Ramos Martinez's Escuela de Pintura al Aire Libre and also at the Academia de San Carlos where he retired in 1954.
Some of his most notable works are the monumental Cristo Rey that stands atop the Cubilete mountain in Guanajuato, Fray Juan de San Miguel which can be seen in the colonial town of San Miguel de Allende and his carved wood bust that is on display at the Brooklyn Museum. Fidias Elizondo died on January 3, 1979 leaving a legacy as one of the best sculptors in the history of Latin American art.