Voter turnout in the mineral-rich landlocked southern African nation was reported to be good, the Lusaka Times reported. Zambia, unlike some of the other sub-Saharan African nations, has enjoyed relative peace and stability for decades.
The polling was proceeding calmly with long queues at various polling stations, the Times reported.
The Wall Street Journal reported police remained on duty across the country with Inspector-General Francis Kabonde saying every effort was being made to avoid violence, which has hit elections in several sub-Saharan nations in recent years.
"We are in charge of the situation, we have enough personnel in all townships, streets and villages," Kabonde said.
Concerns about violence had risen because of competition between Banda and challenger Michael Sata.
Analysts told the Journal they expect Banda to win as an alliance between Sata's Patriotic Front and the United Party for National Development failed to hold. Sata's party also had alleged the ruling Movement For Multiparty Democracy planned to rig the polls.
"I must warn all those wanting to rig the poll that they will have to prepare for the consequences of such acts," Sata said in the statement.
Police were under strict orders to arrest anyone found to be carrying any weapon.
Banda is credited with reviving the country's copper mining sector and helping Zambia take its place among the World Bank-ranked middle-income countries.