Undusk graduated from the Leningrad Oblast School of Cultural Studies in 1940, and started working as a club manager.
During World War II, he joined the Estonian Shooting Corps.
In 1955, he was promoted to the head of the propaganda and agitation department of the Communist Party of Estonia Central Committee.
The organization served as a promoter of foreign policy and as a proponent of Estonian Soviet-era achievements.
He oversaw the opening of the passenger ferry between Tallinn and Helsinki, Finland in 1965.