Mary Eveline Fincken was born on 27 April 1882 in Hoyland, Yorkshire, England. She was the eldest daughter of Christopher William Fincken and his wife. She was born of a musical family. Her grandfather and his sons were amateur organ builders and musicians; her father was a fine amateur organist. Her mother's family included a number of singers in choral societies in northern England, one of her aunts being a singing teacher. She attended school at Sheffield and Manchester where she distinguished herself as a talented singer. At the age of seventeen, in 1899, she won a gold medal at an eisteddfod in Manchester and this made her decide on a singing career.
In 1903 she was appointed assistant teacher at Gunnusbury High School in London. In the same year she won a scholarship to study singing at the Royal Academy of Music (RAM), obtaining the LRAM (Licentiate of the Royal Academy of Music) in 1905. In the same year she made her debut in a concert with the Queen's Hall Orchestra conducted by Henry Wood.
A series of engagements in London and other parts of England followed, including a performance as soloist in Elijah. She also obtained an appointment as singing mistress at Wentworth Hall, a ladies' finishing school. The English climate was seriously affecting Fincken's health, however, and she was advised to visit South Africa. She arrived in 1908 and eventually decided to settle here. Shortly after her arrival in 1908 she sang in the Cape Town City Hall. Later she also sang in other major centres in the interior, such as Bloemfontein which she visited in October and November 1911. In Cape Town Fincken was one of the first staff members of the South African College of Music. When the college was incorporated into the South African College (University of Cape Town) in 1912, she was appointed senior lecturer in singing. Among her distinguished pupils were Cecilia Wessels, Jessie Sonnenberg and Albina Bini. She devoted herself increasingly to education, arranging music education tours under the aegis of the Education Department, and later also university extension courses in music which were coupled with concert tours to various Cape centres.
From the proceeds of these concerts she established the first overseas scholarships for students at the college. Closely linked to her educational work was the Melodic Society which she founded in 1911 and of which she was the life president, as well as the Eveline Fincken Ladies' Choir which she created and conducted. She was also a co-founder of the Women's Business and Efficiency Club. In recognition of her advancement of a musical culture in South Africa, the RAM conferred on her an honorary ARAM (Associate of the Royal Academy of Music) in 1920. She was a member of the New Education Fellowship, as well as a member of the South African Society of Music Teachers for which she organized the music section during the World Conference in South Africa in 1932.
When her health started failing Fincken retired from the college in 1935. Before returning to England she gave a farewell concert in the Cape Town City Hall. In London she opened two hostels, called the Clarendon Clubs, for overseas students. These hostels were, however, bombed during the Second World War (1939-1945). She returned to South Africa in 1943 and resumed teaching singing, revived her ladies' choir and arranged concerts. She bequeathed her collection of music to the black section of the Cape Town Public Library. The South African Broadcasting Corporation paid tribute to her pioneering work as an artist of the microphone from 1924 when broadcasting started in the Cape. She died on 15 June 1955 in Cape Town.