More than 82,000 people have applied to a program that allows young illegal immigrants to stay in the U.S., the Department of Homeland Security said Friday, and more applications are expected as potential beneficiaries wrestle with the paperwork-intensive process.

U.S. Citizenship and Immigration Services, a unit of Homeland Security, began accepting requests for the program, known as "deferred action for childhood arrivals,' or DACA, on Aug. 15, and approved 29 applications in the first month. Another 1,600 applications are...