The crowds outside the cathedral in central Cairo carried crosses and portraits of Shenouda.
"Ya Allah!" or "Oh God!" they chanted in unison.
Tragedy struck during the day as three mourners suffocated to death in the crowded church, said church official Anba Younnes.
Soldiers backed by armored personnel carriers deployed outside the cathedral, possibly as a deterrent to possible attacks by Muslim extremists targeting the large number of Christians gathered or angry over the traffic disruptions they caused.
Shenouda, seated on the throne of St. Mark, or Mar Morkos, was clad in the elaborate regalia he traditionally wore to oversee services. With his head slightly tilting to the right, he held a scepter.
"Please, let me come a little bit closer," one woman pleaded to guards surrounding the body to keep the mourners away.
Field Marshal Hussein Tantawi, who heads Egypt's ruling military council, visited the church with other generals and consoled Coptic leaders.
During his 40 years as patriarch, Shenouda, long a supporter of ousted President Hosni Mubarak, strove to ensure his place among the main players in this mainly Muslim nation, pressing demands behind the scenes while keeping Christians' anger over violence and discrimination in check.
It was a delicate balancing act undertaken for years by a man who kept a relatively high media profile.
Shenouda's death could lead to a long power vacuum.
It could take months before a successor is found, according to Fuad Girgis, a prominent Christian from the Mediterranean city of Alexandria and a member of the church's local layman council.
"Pope Shenouda assumed the throne of St. Mark eight months after the death of his predecessor," he noted.
Shenouda will be buried Tuesday.