Josefa Cummings Lydman, 57, a former specialist in public affairs at the State Department, died of cancer Wednesday at George Washington University Hospital.

She had worked in the office of public affairs at State for nine years before leaving this country in 1956 to accompany her husband, Jack W. Lydman, a career Foreign Service officer, on a series of assignments overseas.

They lived in Bangkok, Surabaya, Jakarta and Canberra. Their last post was in Kuala Lumpur, while he was ambassador to Malaysia. They returned here after his retirement in 1974.

Born in Hartford, Conn., Mrs. Lydman graduated with honors from Hunter College in New York City. In 1942-43, she worked for the War Department there.

She then moved to Washington, where she was in charge of public affairs for the Office of Strategic Services.

In 1944, Mrs. Lydman left government service to join the Gallup Poll in Princeton, N.J., where she was in charge of public opinion analysis and research for Seventeen Magazine. She returned to Washington after her marriage in 1946.

She was a member of the Woman's national Democratic Club and an associate of the Cosmos Club and the Army and Navy Club.

In addition to her husband, of the home in Washington, she is survived by two brothers, Edward Cummings, of Huntington, N.Y., and JOthn Chencski, of Brewster, N.Y., and four sisters, Florence Palandrani and Helen Cummings, both of Huntington, Janina Wilcox, of Long Beach, Calif., and Leokadia Sari, of Convent Station, N.J.