Eucla Stevens was named after the Western Australian town of his birth. He grew up in Claremont which is where he learnt to play soccer and played for the local team as a junior.
Private Stevens served in the 4th Division Cyclist Company and was transferred to the 32rd Battalion where he saw out the remainder of the war.
Upon his return he joined the powerful Perth City United club that were crowned champions in 1922. In 1923 he moved to Albany where he kept playing and was appointed Vice President of the club in 1924. By 1926 he had moved to the wheatbelt town of Ardath and kept playing in the district into the 1930s.
In 1932 he married Elsie Harris. Eucla Stevens passed away in Perth in December 1967 at the age of 72.