Forty-five political parties, most of them small ones, are taking part in the race.
Sudanese president Omar Al Bashir stressed that he will bring an end to the state of war in the country.
Al Bashir says establishing peace is the first item on his campaign agenda, adding that the areas including the Blur Nile, South Kurdufan and Darfur will live in peace again.
The ongoing war there has left thousands of people dead and has crippled the economy.
Some Sudanese hope the elections will bring positive changes to the country.
Mohamed Osman, a local resident in Khartoum says: "We hope the current high prices, expensive living and unemployment would change, there must be reform for the sake of the youth and freedom."
The polling process is to last until Wednesday while the vote counting is set to begin the next day.
The final results of the elections are scheduled to be announced on April 27.
