Willi (Wilhelm Josef) Soukop was born in Vienna, Austria-Hungary (now Austria) on 5 January 1907, the son of an Austrian mother and a Moravian (Czech) shoemaker-father, who committed suicide soon after returning from the First World War. To help support the family, Soukop learned to carve umbrella handles and other ivory objects for a local trader, a task at which he became very skilled. He went on to train at Vienna Academy of Fine Art, as a pupil of Josef Müllner. In 1934, taking up a chance invitation to Dartington Hall, Devon, which had become a refuge for many artists escaping Nazi persecution, he settled into a flourishing cultural community, also meeting there his future wife, the French dancer Simone Michelle (née Moser 1916–1993). He had his first solo show in 1939 at the Stafford Gallery in London, which included his pink cement head of Polish dancer Pola Nirenska (Ben Uri Collection), sculpted at Dartington, where he had a solo exhibition in March 1940. In June, following the introduction of internment for so-called 'enemy aliens', he spent nine months in a Commonwealth interment camp in Ottawa, Canada, before returning to Dartington, where he was commissioned to carve the swan fountain.

Afterwards, he established a successful sculpture department at Blundell’s School in Tiverton, Devon, then at Bryanston school in Dorset, and the Downs, Worcestershire. He also taught at Dartington and at Guildford School of Art, where his pupils included Elisabeth Frink, who followed him to Chelsea School of Art. In 1969 Soukop was appointed Master of Sculpture at the Royal Academy schools and exhibited at the Royal Academy on more than 70 occasions. His sculpture was commissioned for many public spaces, including the Elmington Estate in Camberwell, Loughborough University and the University of Hull, and his well-known Donkey sculpture, first executed at Dartington, was recast for Pittmans Field, Harlow, Essex.

Willi Soukop died in Glasgow, Scotland on 8 February 1995. His work is in UK public collections including Abbot Hall, the Ben Uri Collection, the Red House, Aldeburgh, the Royal Academy of Arts, Tate, and the University of South Wales Art collection.