Phan Xuan Vu, 19, and Le Van Hoa, 20, passed the medical examination for military service earlier this year, and were ordered to report at the military headquarters of the province's Nghi Xuan District on February 7 for being formally deployed.
Authorities in Xuan Thanh Commune, where Vu lives, said they have sent officials to his house several times but they have been unable to meet him. His parents have reportedly said he is "doing business in a faraway place" without saying where.
Hoang Van Ha, chairman of Cuong Gian Commune, where Hoa lives, said he has not provided a reason for failing to turn up but could not be found either.
Authorities said Tuesday they would summon the two men's parents to pay the fines, track the duo down and tell their families to encourage them to return home and report for duty.
In January Can Loc District authorities had fined 29 people for not turning up for the medical. Most were found to be doing business either in southern Vietnam or abroad.
Compulsory enlistment has existed in Vietnam since the end of the Vietnam War in 1975 and thousands of young people join the army every spring. Men aged between 18 and 25 years old have to serve two years, while women can volunteer.