Unwin worked as a shipwright, but from childhood he showed an interest in a variety of materials and the creative manipulation of materials. In 1986, he apprenticed in the study of stone carving at Pietro Santa, Carrara, Italy.
Upon his return to Victoria he exhibited in a solo show at Open Space Gallery. His work was exhibited in 1990 at Le Jardin de Sculpture in Laval, Quebec. Unwin's sculptures attracted much acclaim and he received commissions for sculptures to commemorate the 50th anniversary of Royal Roads University and to create a public sculpture for the Victoria Police Department.
Jay Unwin was killed in a car accident in 1996.