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She was born Elizabeth May Ramsay Tannock, the daughter of Elizabeth Mary (née Ramsay), and Archibald Tannock. Her father was a confectioner. She was born and grew up in Geelong, and was educated to matriculation level at the Girls' High School. She matriculated in 1895. After a period of teaching at the Methodist Ladies' College and Tintern, another independent girls' school, she moved to Perth, Australia in 1916 to complete a Bachelor of Arts degree at the University of Western Australia, which offered free education. Her major interests were political science, constitutional law and economics.
In 1917, aged 41, she married businessman Claude Couchman, but they had no children. He died ten years later. On his death she decided to devote the rest of her life to the pursuit of public interests, which included voluntary work and the duties of a Justice of the Peace. She went on to devote her life to working in the public sphere. She was President of the Australian Women's National League, a conservative women's organisation established in 1904 to support the monarchy and empire, to combat socialism, educate women in politics and safeguard the interests of the home, women and children, from 1927 until 1945. During the inter-war years it claimed 40,000 members and was the largest continuing non-labour organisation, but those numbers dwindled to approximately 12,000 by 1944. In 1945 it merged to help form the new Liberal Party of Australia. Elizabeth Couchman insisted on equal representation of women and men at all levels of the Victorian division, and was involved in establishing the branch structure of the party. She worked in the Liberal Party organisation as a member of the state executive and state council and served as Victorian vice-president of the party from 1949–1955.
Like many politically active women of her generation, she was denied the opportunity to gain a safe seat in the national parliament. She sought pre-selection for the Senate on three occasions, but was unsuccessful. She eventually gained pre-selection to stand in the safe Labor seat of Melbourne in the 1943 election, but lost. Nonetheless, she mentored others such as Margaret Guilfoyle, who came after her and who was elected to the Senate in 1970. Couchman wanted women to be able to participate fully in the political process; to run for office and to do much more than the 'political housework'.
- Who's Who in Australia, 1974
- 200 Australian Women