Long queues formed in several areas, including Kampala, after polling stations opened late and materials arrived hours after the planned start. Some voters reported faulty biometric machines, adding to frustration.
President Yoweri Museveni, in power since 1986, is seeking another term against seven challengers, including opposition figure Bobi Wine, who has called for political change.
Authorities shut down the internet earlier this week, citing security concerns, a move criticised by rights groups and businesses alike.
Soldiers and police were visible across the country as officials urged calm while ballots were cast.