People lined the streets to watch the procession, singing old songs from the struggle against the apartheid regime and calling out their farewells to Mandela, who died Dec. 5 at the age of 95.
Police blocked traffic, backing up cars for several kilometers (miles) on a highway leading into Pretoria.
Army helicopters had been circling overhead but then a sudden quiet fell over the amphitheater as the hearse arrived.
Eight warrant officers representing the various services and divisions of the South African National Defense Force carried the casket, led by a military chaplain in a purple stole.
The officers set down the coffin and removed the flag.
Officials have banned cameras from the viewing area and asked people to turn off their mobile phones.
Mandela's body will lie in state for three days at the Union Buildings, which the South African government describes as a “modern-day acropolis” atop a hill overlooking Pretoria.
The architect who designed it envisioned its two wings, made of half a million cubic feet (14,100 cubic meters) of stone, representing the Afrikaans and English languages spoken in the country—but none of the land's native languages.